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Full text of "Investigation of the air lift pump"

UNIVERSITY 
OF FLORIDA 
LIBRARY 




BULLETIN OF THE UNIVERSITY OF WISCONSIN 



NO. 450 

Engineering Series, Vol. e, No. 7, pp. 405-573 



AN INVESTIGATION OF THE AIR LIFT PUMP 



BY 

GEO. JACOB DAVIS, Jr., C. E. 

Assistant Professor of Hydraulic Engineering 
The University of Wisconsin 

AND 

CARL ROBERT WEIDNER, C. E. 

Instructor in Hydraulic Engineeri/ng 

The University of Wisconsin 



RESEARCHES IN HYDRAULICS 
Daniel W. Mead, Professor in Hydraulic and Sanitary Engineering 



MADISON, WISCONSIN 
October, 1911 
PRICE 40 CENTS. 



4 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Entered as second-class matter June 10, 1898. at the post office at Madison. Wisconsin 
under the Act of July 16. 1894 



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Walter M. Smith. Chairman 
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THOMAS K. Ubdahl, Economics and P litical Science Series 

WILLIAM H. Lightv. University Extension Series 

William S. Marshall, Science Series 

DANIEL W. MEAD. Engineering Series 

R. E. NEIL DODGE, Philology and Literature Series 

Winfred T. ROOT, History Series 



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Wis. 



CONTENTS 



Page 

Introduction 13 

Development of the air lift pump 15 

Principle of the airlift pump 18 

Theory of the air lift pump 20 

Echol's theory 20 

Harris's theory 20 

Anderson's theory 23 

Gibson's theory 24 

Lorenz's theory 24 

Green's theory 29 

Methqd of operation 31 

Description of an air lift pumping plant 32 

The pump 32 

The eduction pipe 32 

The foot-piece 32 

The tail-piece 34 

Side inlet pump 34 

Annular air tube pump 34 

Central air tube pump 36 

Combination pump 37 

Multiple air lift pump 37 

Return air pump '. 38 

Diverging outlet pump 39 

The plant 40 

The compressor 40 

The receiver 40 

The air line 40 

Disadvantages of the air lift pump 42 

Low efficiency 42 

Great depth of submergence 42 

Limited horizontal pumping 42 

Aeration 43 

Advantages of the air lift pump 44 

Large capacity 44 

Low maintenance cost 44 

Low operating cost 45 

Not affected by high temperatures 45 

Aeration 45 

Reliability 45 



4 



CONTENTS 



Wisconsin Experiments 

Page 

Notation 47 

Description of apparatus— 1908 experiments 48 

The eduction pipe 48 

The foot-piece 48 

The tail-piece 48 

The water supply 52 

The air supply 52 

The air measurement 53 

Description of apparatus — 1909 experiments 57 

The well 57 

The eduction pipe 57 

The foot-piece 57 

The tail-piece 58 

The water supply 58 

The air supply 60 

The gages 60 

Leakage tests 60 

Methods of observing 61 

1908 experiments 61 

1909 experiments 62 

Methods of computing 65 

Quantity of air 65 

Theoretical work done by air 68 

Quantity of water 69 

Submergence 70 

Actual work done in lifting water 71 

Efficiency 71 

Ratio of volume of air to volume of water 71 

Velocity of water in a li-inch tail-piece 72 

Experimental coefficient 73 

Loss due to friction in air pipe and air nozzle 73 

Loss of head due to entrance 75 

Loss of head due to velocity of discharge 75 

Loss of head due to elbow 76 

Loss of head due to pipe friction and slip 76 

Experimental relations 81 

Relation of discharge to air used 81 

Relation of output to percentage of submergence 83 

Relation of efficiency to input and percentage of submergence 

with constant length of pump 90 

Efficiency and input 91 

Efficiency and percentage of submergence 92 

Relation of efficiency to input and percentage of submergence 

with constant lift 93 

[408] 



CONTENTS 5 

Experimental relations — Continued Page 

Efficiency and input 94 

Efficiency and percentage of submergence 94 

Relation of discharge and efficiency to lift 95 

Effect of compressed air outside of pump 100 

Effect of type of foot-piece 105 

Effect of diverging outlet 107 

Study of the size of air bubbles 109 

Results of previous experiments 112 

Brown and Behr's experiments 112 

Josse's experiments 112 

Kelly's experiments 113 

Darapsky and Schubert's analysis of experiments 114 

Westinghouse Air Brake Company's experiments 115 

Duty tests 117 

Conclusion 119 

Data 121 

Bibliography 161 



[409] 



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ILLUSTRATIONS 



Page 



Fig. 1 Diagrams for illustrating the principle of the air lift pump 18 

2 Diagrams for illustrating the theory of the air lift pump. . . 21 

3 Comparison of the Frizell and Pohle systems of operation. 25 

4 Frizell's foot-piece 33 

5 Pohle's foot-piece 33 

6 Different methods of piping wells 35 

7 Multiple air lift 38 

8 Air-separator 38 ' 

9 Air lift pumping plant 39 

10 Experimental apparatus — 1908 experiments 49 

11 Foot-pieces used in Wisconsin experiments 50 

12 Foot-pieces used in Wisconsin experiments 51 

13 Drum and orifice for air measurements 53 

L4 Gages used in 1909 experiments 55 

15 Experimental apparatus — 1909 experiments 59 

16 Coefficient of discharge for air orifice • 66 

17 Curve for computing discharge of air through orifice 67 

18 Curve for finding energy per pound of air at various pres- 

sures 70 

19 Loss due to friction in air pipe and air nozzle 73 

20 Coefficient of pipe friction and slip 80 

21 Relation of discharge to air used 82 

22 Relation of air used to percentage of submergence 84 

23 Relation of output to percentage of submergence 85 

24 Relation of output to percentage of submergence 86. 

25 Relation of quantity of air used to maximum output and to 

percentage of submergence 87 

26 Logarithmic plotting of output — percentage of submerg- 

ence curves 89> 

27 Relation of efficiency to input with constant length of pump 90' 

28 Relation of efficiency to input with constant length of pump 91 

29 Relation of efficiency to percentage of submergence with 

constant length of pump 92; 

30 Relation of efficiency to input with a constant lift 93 

31 Relation of efficiency to percentage of submergence with a 

constant lift 94 

[411] 



8 



ILLUSTRATIONS 



Page 



Fig. 32 Relation of discharge and efficiency to lift 95 

33 Relation of discharge and efficiency to lift 96 

34 Relation of discharge to lift, with constant input 99 

35 Curves showing effect of compressed air outside of pump. 101 

36 Curves showing effect of compressed air outside of pump. 103 

37 Curves showing effect of compressed air outside of pump. 104 

38 Curves showing the effect of the type of foot-piece 106 

39 Curves showing the effect of the type of foot-piece 107 

40 Curves showing the effect of a diverging outlet 108 



[412] 



LIST OF SYMBOLS 



Areas 

area of orifice in square feet. 

area of eduction pipe in square feet. 

Coefficients 
coefficient of pipe friction and slip (variable), 
coefficient of entrance, 
coefficient of discharge of orifice, 
coefficient of pipe friction and slip (average). 

Efficiency 

efficiency. 

Distances 

head. 

head produced by the air used, 
elevation of outlet above datum, 
elevation of point above datum, 
head lost at entrance, 
elevation of inlet above datum, 
lift, in feet. 

head lost due to elbow. 

head lost in eduction pipe due to pipe friction and 
depth of submergence in feet. 

[413] 



10 



LIST OF SYMBOLS 



Work 

L = total work, per pound of air, in foot pounds. 

1 = work output, in foot gallons per second. 

1. = work input, in foot pounds per second. 

1 = maximum work output, in foot gallons per second. 

1 = work output, in foot pounds per second. 

Pressures 

p = absolute pressure at any point, with variable specific weight of 
air. 

p = loss of pressure due to air friction, when discharging into the- 
atmosphere. 

P b = barometric pressure, acting on the surface of the water in the-- 
well and also on the discharge end of the pipe A (Fig. 3). 

p = absolute pressure at the point C (Pig. 3). 
c 

p^ = absolute pressure of air at downstream side of orifice, in pounds- 
li per square inch. 

Pg — absolute pressure at gage. 

p. — absolute pressure at inlet in the foot-piece. 

p s = standard atmospheric pressure (=14.7 pounds per square inch). 

p — absolute pressure of air at upstream side of orifice, in pounds- 
u per square inch. 

p — loss of. pressure due to air friction when discharging against the- 
pressure p. in the foot-piece. 

p^ — absolute initial pressure of air, in pounds per square foot. 

p s = absolute final pressure of air, in pounds per square foot. 

Volumes 

Q. = volume of air at pressure p., in cubic feet. 

Q = volume of air at standard atmospheric pressure (14.7 pounds, 
per square inch). 

q = discharge of free air, in cubic feet per second, 
a 

q^ = discharge of air at pressure p^ 

q — - discharge of water in gallons per minute.. 

[414] 



LIST OP SYMBOLS H 

discharge of water, in cubic feet per second, 
volume of air at pressure p^ 
volume of air at pressure p i . 
volume of air at pressure p g . 

Submergence 
percentage of submergence. 

percentage of submergence corresponding to maximum dis- 
charge. 

Temperature 

absolute temperature at upstream side of orifice, in degrees- 
Fahrenheit. 

Densities 

density of mixture of air and water, variable. 

density of air at 14.7 pounds per square inch pressure. 

density of air at the discharge end of the eduction pipe. 

density of air at inlet in foot-piece. 

density of air, variable. 

density of fluid pumped. 

the ratio of compression in atmospheres. 

Velocities 

variable velocity. 

velocity of air in pipe, when discharging into the atmosphere. 

velocity of the mixture of air and liquid, at the outlet of the 
eduction pipe, in feet per second. 

velocity of water in the well outside of the eduction pipe at 
point c (Fig. 3). 

velocity of the liquid in the eduction pipe below the air inlet, 
velocity of the liquid in the tail-piece. 

velocity of air in pipe, when discharging against pressure p.. 
Weights 

weight of air used in pounds per second, 
weight of water pumped in pounds per second. 

[415] 



INTRODUCTION 



The air lift method of pumping, though not highly efficient 
as compared with some other methods, is nevertheless an im- 
portant one, owing to the many advantages it possesses over 
other methods in the pumping of corrosive liquids, in pumping 
large quantities from wells of small bore, and on account of 
other features which will be discussed on a succeeding page. 

Notwithstanding the fact that this method of raising liq- 
uids has been known for over a century and is now quite ex- 
tensively used in both small and large pumping installations, 
the amount of reliable data, that are available to the practic- 
ing engineer, concerning the performance of this type of 
pump, is very meagre. Numerous tests of air lift pumps have 
been made by the manufacturers of air compressors and pat- 
ented devices to be used in connection with air lift pumping 
plants, but the information gained from such tests has not 
been made public. The engineer in private practice has avail- 
able, for use in designing, only the data from some tests on 
very small scale apparatus and those from a number of tests 
on actual installations, where it was not practicable to vary 
the conditions of operation much, nor to make accurate meas- 
urements of quantities. 

With the purpose of supplying the demand for reliable 
data, from tests on pumps of commercial size and of various 
types, the investigations described and discussed in this bulle- 
tin were undertaken. The experiments, which comprise more 
than 600 runs, were carried on in the Hydraulic Laboratory 
of the University of Wisconsin. In taking the data on the 
first 318 runs the writers were assisted by B. R. McBride, then 
Instructor in Hydraulic Engineering, who supervised the work 



[417] 



14 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



of C. J. Miller and E. J. Springer, then senior students in the 
College of Engineering, who used the data taken by them as 
the basis of a thesis for the baccalaureate degree. Assistance 
in the way of computing, drafting, and changing apparatus, has 
also been given from time to time by E. P. Abbott, G. P. Stocker, 
M. C. Koenig, E. B. Nelson, P. C. Dodge, Andrew Ludberg, and 
R. W. Hart, students in the College of Engineering. The ob- 
servations on runs 319 to 500 inclusive were made by the writers, 
those from 501 to 608 inclusive were made by Messrs. Bingham 
and Hallauer, who included these data in a thesis submitted for 
a degree. 

The experiments were not made on actual wells, but the 
apparatus was designed to reproduce as nearly as possible the 
practical working conditions of the air lift pump. 



[418] 



HISTORICAL NOTES ON THE DEVELOPMENT OF THE 
AIR LIFT PUMP 



The application of compressed air as a means of pumping 
liquids was first used by Carl Emanuel Loscher, a German 
Mining Engineer, who in 1797 made some laboratory experi- 
ments, and described his invention in a pamphlet entitled 
"Aerostatisches Kunstgezeug. " It was not until half a cen- 
tury later that the. idea was put to a practical application, 
and then in a completely independent manner, by an Ameri- 
can named Cockford, who in 1846 succeeded in pumping pe- 
troleum from some wells in Pennsylvania. 

On May 23, 1865, a United States patent (No. 47,793) was 
issued to A. Brear on an "oil ejector," which the description 
and illustration accompanying the patent show to have been 
an air lift pump of the annular tube type (see page 34). 

The idea was again revived by Mr. J. P. Prizell who ob- 
tained a patent on an air lift pump, dated Oct. 19, 1880. His 
invention was apparently made independently and without 
knowledge of the work done in this field by others, and grew 
out of his invention of a method of compressing air on which 
he was granted a patent on January 29th, 1878 (No. 199,819). 

The Frizell method of compressing air consists in introduc- 
ing the air within a column of water descending through a 
vertical shaft or pipe, from whence the mixture flows through 
a horizontal tunnel at the top of which the air is collected by 
means of a suitable receiver and from which it may be con- 
ducted to any desired point by a pipe. The water divested of 
the air passes through the tunnel and rises to the surface 
through an ascending shaft at the other end. The invention 
was based on the knowledge that air drawn into a current 
of water, descending through a vertical shaft or pipe with a 

[419] 



16 



BULLETIN OP THE UNIVERSITY OF WISCONSIN 



velocity greater than that with which air bubbles would rise 
in still water, will be carried down with the descending col- 
umn, and will be subjected to a pressure corresponding to the 
depth attained. The amount of air which may be carried 
down and compressed by a current of water depends upon 
the quantity of water and the difference of head available be- 
tween inlet and outlet of the tunnel. Although the bubbles 
of air are actually moving downward their velocity relative 
to that of the water is upward. They, therefore, have a retard- 
ing effect on the velocity of the water due to fluid friction be- 
tween the air and the water. The larger the quantity of air 
introduced the smaller will be the size of the water passages 
between the bubbles, which, with constant head, will result 
in a slower velocity of the water, until the limit is reached 
when the downward velocity of the water is just equal to the 
relative upward velocity of the air. From observation of 
these facts it was apparent that if compressed air be intro- 
duced at or near the submerged bottom of a vertical pipe in 
sufficient quantity, it will, in rising through the water in 
the pipe, cause the water to acquire an upAvard velocity. Mr. 
Frizell in the specifications of his air lift patent (No. 233,499) 
expressly states that his method of pumping is a reversal of 
the principle of his method of compressing air, and since in 
the latter device the air was admitted in the form of small 
bubbles, so in the pump also it was admitted through a great 
number of small orifices with the object of producing small 
bubbles, so as to aerate the water, as illustrated in Fig. 4. 

The air lift pump was used to increase the discharge of 
flowing wells as early as 1884, a patent (309,214) being is- 
sued Dec. 16th of that year to S. S. Fertig on an annular tube 
type of pump. 

Apparently without any knowledge of the previous inven- 
tions Werner Siemens in 1885 made use of the air lift pump 
for draining a mining shaft near Berlin. In France, Laurent 
in 1885 and Goudry in 1886 used a similar contrivance, which 
they called an "emulseur, " for pumping sulphuric acid. 

The term air lift, as applied to the above described method 
of pumping, was first used by Dr. Julius G. Pohle in the speci- 
fications for his patent (No. 487,639) which was issued Dec. 6, 

[420] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



17 



1892. The chief distinction between this type of pump and 
that of Mr. Frizell lies in the method of introducing the air. 
To use his own words, "The invention * * * consists 
in improved processes and apparatus whereby the compressed 
air is delivered in bulk into the lower end of the water educ- 
tion pipe, and the water and air are caused to ascend through 
said pipe in distinct alternate layers of definite dimensions." 
In the specifications of his patent he explains his understand- 
ing of the working of the pump as follows : 

"I have discovered that when air of suitable pressure is al- 
lowed to enter in a constant stream and in suitable quantity 
into an eduction pipe at or near its lower end when it is sub- 
merged in water while its upper end rises above the water about 
the same distance that its lower end is submerged, the com- 
pressed air thus introduced will at first expel the standing 
water from the pipe in an unbroken column free 
from air, and subsequently, by the continued inflowing of the 
compressed air under a pressure just sufficient to overcome the 
resistance of the water outside of the eduction pipe, it will ar- 
range itself in alternate layers with the water, while the latter 
flows into the lower end of the eduction pipe by force of grav- 
ity until it is discharged at the upper or exit end of the pipe. 
This alternate interposition of determinate quantities of air be- 
tween the also determinate quantities of water elongates the 
entire column of air and water, thus facilitating, without 
materially adding to the weight of the column, the discharge of 
the water at a higher level than would be the case were these air 
sections or layers absent. I have also discovered that under the 
above mentioned conditions the compressed air will not escape 
through the water overlying it, and also that the water over- 
lying the compressed air will not fall back through the under- 
lying air while both are in upward motion, but find that the 
elasticity stored in the compressed air layer, pressing alike in 
all directions, forms a temporary water-tight air piston, which 
lifts the water above it to its final discharge without appreciable 
less by leakage or so called "slip," while this compressed air 
piston after having expended its elastic energy in work of lift- 
ing water is dispelled with only a practically unimportant loss 

2 [421] 



X8 BULLETIN OF THE UNIVERSITY OF WISCONSIN 



of power." In Fig. 3(b) a pump is shown in which the air is in 
large bubbles or pistons. 

In addition to the patents mentioned, many others have been 
granted covering various supposed or real improvements. Some 
of these will be mentioned on following pages in the discussion 
of the features of the pump to which they relate. 

THE PRINCIPLE OF THE AIR LIFT PUMP 

The precise action going on in an air lift pump is not thor- 
oughly known and it doubtless differs under the various con- 
ditions of operation, but the basic principle on which the pump 
works is simple and may be illustrated in the following man- 
ner. 

First, consider a vertical pipe, open at both ends and partly 
immersed in a liquid, as shown in Fig. 1 (a). The liquid will 









































< > 














I 






■ 




* 







(a) lb) (c) 

Pig. I. 

stand at the same height inside and outside of the pipe. As- 
sume that a block of material, like cork or wood, lighter than 

[422] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



19 



the liquid, made to fit the pipe snugly but able to move with- 
out friction, is made to replace part of the liquid near the bot- 
tom of the pipe. The hydrostatic pressure on the underside 
of the block is now greater than the combined weight of the 
block and the liquid above it. The block and the liquid in 
the pipe will therefore be pushed up in the pipe, as shown in 
Fig. 1 (b), until the head h balances the difference between the 
weight of the block and the weight of an equal volume of the 
liquid. If more blocks of the light solid material be introduced 
into the pipe, the liquid will be raised a distance h for each 
block until the top of the pipe is reached, when an overflow of 
liquid and blocks will occur leaving an unbalanced head in the 
pipe, which would keep up the discharge as long as the supply 
of liquid and blocks was kept up at the bottom of the pipe. In 
the Pohle air lift system the claim is made that the pump works 
as described above, with the exception that compressed air is 
used instead of a light solid, and that work is done by the ex- 
pansion of the air as it is relieved of the weight of the liquid 
when approaching the top of the pipe. 

A closer approximation is made to usual working conditions 
in an air lift pump by the illustration (c) in Fig. 1. In this 
case the block of light material, cork, wood, or air, does not 
entirely fill the cross-section of the pipe. By virtue of its 
buoyancy it will tend to rise in the pipe and the liquid in the 
pipe will tend to flow down past it. The height h, to which 
the water rises in the pipe in this case, represents the head 
necessary to force the liquid down through the restricted pass- 
age-way past the block. The same conditions would obtain 
if the single block nearly filling the pipe were replaced by a 
large number of small blocks. It would require some head h 
to overcome the resistance offered to the liquid in its flow be- 
tween the small blocks or between the blocks and the pipe 
walls. If a sufficient quantity of the small blocks of air or 
other light material are inserted, the head h will reach the top 
of the pipe and will cause a discharge of the liquid. The flow 
of liquid down past the buoyant material is called the slip of 
the pump. It is the cause of a serious loss of energy. 

A commonly accepted conception of the principle of opera- 
tion of the air lift pump may be had by considering that the 

[423] 



20 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

air bubbles, in rising through the water in the discharge pipe, 
reduce the specific gravity of the mixture and therefore the 
weight of the column, causing an unbalanced condition between 
the column inside and outside of the tube. The excess pressure 
at the base of the column, due to the external water pressure, 
therefore, forces the mixture above the supply level and out 
of the top of the pipe. This excess pressure increases with the 
depth of submergence of the pipe, and the latter must be regu- 
lated to suit the height of delivery. 

Theory of the Air Lift 

Echol's Theory. — An attempt was made by Professor W. H. 
Echols, to develop a theory of the air lift pump based upon a 
mathematical analysis of the problem. The results of his stud- 
ies were presented before the Philosophical Society of the Uni- 
versity of Virginia in 1891, but they were not available to the 
writers. 

Harris's Theory. — A further effort in this direction was made 
by Professor Elmo Gr. Harris of the University of Missouri, 
with the purpose of obtaining a rational formula by which a 
pump could be designed intelligently, and on which experiment 
could be based. His discussion of the subject was published 
in the Journal of the Franklin Institute, Vol. 140, p. 32, July, 
1895. 

In deriving his formulas for the design of a pump the work 
done by the air is divided into four parts by Professor Harris, 
as follows: 

(1) The kinetic energy in the liquid discharged at the top of 
the pipe. 

(2) The energy necessary to raise the liquid to the top of the 
discharge pipe. 

(3) The energy lost by the liquid slipping down by the bub- 
bles. 

(4) The energy consumed by friction in passing through the 
pipes. 

Theoretical expressions may be found for each of the above 
quantities. That for the slip is too complicated for use in 
practice, so an approximate formula based on a number of as- 

[424] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



21 



sumptions is derived. For the fourth term the value of the 
friction factor is assumed, as is the relation of the loss to the 
velocity. In-as-much as it is not possible to verify the cor- 
rectness of the individual terms for the losses by experimental 
means, since the loss due to slip and that due to friction could 
not be differentiated under working conditions, and in-as-much 
as the formulas are complicated and difficult to use, they will 
not be given in detail, but a brief review of the general prin- 
ciples on which they are based will be presented as a further 
aid to an understanding of the action of the air lift pump. 



























f 




























6 


J 


J 




Q 




J 






(a) 






(b) 





In his consideration of the subject Professor Harris first pro- 
poses the following problem: 

A vertical pipe, open at both ends, is partly immersed in a 
liquid, as shown in Fig. 2 (a). A quantity of gas is released 
within the pipe and below the surface of the liquid. What ef- 
fect will the gas have on the column of liquid and what will be 
the action of the bubble of gas ? 

The pipe is assumed to be so large that capillary forces can- 
not control the action. Then the bubble will ascend in the 

[425] 



22 BULLETIN OP THE UNIVERSITY OF WISCONSIN 

pipe. Assuming for the present that no liquid is pumped out 
of the top of the pipe, then during the ascent the liquid above 
the bubble must pass by it in order to get below. Hence, the 
bubble cannot occupy the whole cross-section of the pipe. In 
order to ascend the babble must become elongated until the li- 
quid can pass down. In order to pass down through the contrac- 
tion formed by the bubble, the liquid must have a certain abso- 
lute velocity. The presence of this velocity is evidence of the 
existence of an unbalanced head somewhere above. 

Expressions are found for the upward velocity of the air bub- 
bles and for the downward velocity of the water, and from the 
relations of these quantities the area of cross-section of the bub- 
ble and the rate of loss of liquid from above to below one bub- 
ble is computed, thereby giving a basis for finding the loss of 
energy due to slip. 

Under the conditions of the above problem all of the useful 
energy supplied by the air is wasted in fluid friction caused by 
the water slipping past the bubble. 

A closer approximation to working conditions is illustrated in 
Fig. 2 (b), in which the arrangement is the same as in the pre- 
ceding problem with the exception that the top of the pipe is 
flush with the surface of the supply reservoir. In the first prob 
lem the bubble produced the standing head h. In the absence 
of the standing head in this problem, the liquid will flow out of 
the top of the pipe with a velocity theoretically equal to V2gh. 
Under the conditions of this problem the entire column of liquid 
in the pipe will be moving upward. The downward velocity of 
the water past the bubble will not be actual but only relative to 
the velocity of the bubble, but the loss due to slip is assumed 
to be the same as under the conditions of the first problem. 

In air lift pumps as actually operated the bubbles are not 
always of the proper size to fill the pipe in the manner assumed 
above. In the pump specified in the Frizell patent, for example, 
the air is admitted to the water, as already described, in the 
form of very minute bubbles. When the size of the bubble is 
small the surface tension in the liquid tends to compress the 
bubble into a sphere. "When the bubbles are small their motion 



[426] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



23 



is irregular and the formulas deduced by Professor Harris for 
loss due to slip are not supposed to hold. 

In his book on Compressed Air, published in 1910, Professor 
Harris has modified his original theory, and shows that the slip 
varies as the square root of the volume of the bubble, and that 
the head produced is independent of the size of the bubbles, 
hence it would seem desirable to have the air in the form of small 
bubbles. 

Anderson's Theory. — A simple theory of the air lift pump, 
proposed by Mr. Robert M. Anderson, was published in Bulletin 
No. 53 of the Hudson Engineering Company in 1905. In de- 
veloping this theory static conditions were assumed to exist in the 
pump. Under such conditions the pressure at the air inlet due 
to the depth of submergence is equal to that produced by the 
mixture of air and water in the eduction pipe. The lift is 
found by computing the length of eduction pipe required to give 
a pressure equal to that due to the submergence. This length is 
inversely proportional to the average density of the mixture. 
Tc find the latter quantity an expression is developed for giving 
the mean volume of the air, while expanding isothermally from 
its volume at the inlet to its volume at atmospheric pressure. 
The various terms when combined give the volume of air at 
barometric pressure required to pump one volume of water, as 

h 

%=- (1) 

s lo £e 

55 p — p P 

in which 

q b — - discharge of free air at the pressure p b . 
hi = the lift, in feet. 
h s — the depth of submergence, in feet. 
p b = barometric pressure. 

Pi = pressure at the air inlet in the foot-piece. 

For convenience of reference these and all other symbols used 
in this bulletin have been tabulated and denned on page 9. 

Under the static conditions assumed for developing this theory, 
there would be no losses of head, such as those occasioned by en- 
trance to the eduction pipe, pipe friction, slip, elbow loss, etc., 

[427] 



24 



BULLETIN OP THE UNIVERSITY OF WISCONSIN 



and accordingly no terms for these quantities are found in the 
formula. To adapt the formula for practical use a constant, 
found by comparing with experimental results, has been intro- 
duced giving 

h 

q b = i.9 1 (2) 



p, p. 

p l- p b p b 



It is not claimed that this formula gives accurate results, but 
only approximations. 

Gibson's Theory. — This theory, published in 1908 by A. H. 
Gibson in his ' ' Hydraulics and Its Application, ' ' is based on the 
same fundamental ideas as the preceding one except that it is 
not confined to static conditions. Under operating conditions 
the column of mixed air and water in the eduction pipe is not 
long enough to create a pressure at the air inlet sufficient to bal- 
ance that clue to submergence, the difference being made up in 
the losses of pressure due to friction, etc. Mr. Gibson takes ac- 
count of the losses due to friction and velocity at exit, introduc- 
ing terms for the loss of head due to these causes so that formula 
(1) becomes 

h + h + J 

= . 1 P 2 g (3) 

P P 

s lo £e 

P — P P 

Lorene's Theory. — A very simple mathematical theory, ex- 
plaining the action of the air lift pump, was published by Dr. 
IT. Lorenz, in Zeitschrift des Vereines Deutcher Ingenieure, Vol. 
53, page 545, April, 1909. The formulas he deduces take account 
of the losses of energy occasioned by slip, pipe friction, etc., and 
are therefore of practical use in designing air lift pumps, pro- 
vided the necessary experimental coefficients are known. The 
theoretical discussion in Dr. Lorenz 's article is therefore given 
in full below. Let 

Pj = the pressure in the foot-piece. 

p b =the barometric pressure acting on the surface of the 
water in the well and also on the discharge end of the 
pipe A, Fig. 3. 

[428] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



25 



n w = the density of the fluid pumped. 
w w = the weight per second of the water pumped. 
w a = the weight per second of the air discharged through the 
pipe B. 

Ui = the density of the air at the air inlet in the foot-piece. 




(a) (b) 
Pig. 3.— Comparison of the Prizell and Pohle Systems of Operation. 

u b = the density of the air at the discharge end of pipe A. 
Vj = the velocity of the liquid in the pipe A below the air in- 
let. 

c e = the coefficient of entrance. 
h s = the depth of submergence. 

Eef erring to Fig. 3 (a), it may be seen that during the opera- 
tion of the pump the following equation of heads holds between 

[429] 



26 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



the point C in the pump and a point at the same elevation out- 
side the pump : 

s u 2g \ e/ w 

w 

For flow in the discharge pipe A the following differential 
equation holds on account of the variable value of the density u 
of the mixture of gas and liquid: 

u g 

in which v equals the variable velocity, and p the pressure at 
any point; and with the variable specific weight of air as u v , 
equation 

W _i_ w w w 

a w = + _i (6> 

u u u 

V w 

designates the momentary volume of the mixture w a + w w . 

If the mixture of air and fluid is very intimately commingled ; 
that is, if the air penetrates the fluid in the form of small bub- 
bles, it can be assumed that the air expands isothermally, so 
that 



u _ P u 

v — b 



(7) 

P b " 

By means of equations (6) and (7) the fundamental formula 
(5) becomes 

Wa P * dp Ww dp vdv 3 ^ 
dh — = — c v 2 dh (8> 

w _i_ w up w _j- w u g 

a 1 w b a 1 w w 

Integrating this equation between the limits h s + hi and 7 
Pi and p b , and Vi and v b (the velocity of the mixture at the dis- 
charge end of the eduction pipe) there results 

w p p w r p pi 

_C h +h ) + — t 5 iog e _i + »■ 1 " J 

V & / W _1_ w u p 



_i_ w u p W _L w u 

' w b b a 1 w w 



V 2 V 2 

b " + 



2g 

[430] 



J c v2 d h 



DAVIS & WEIDNER— THE AIR LIFT PUMP 27 

Replacing the last term in this equation, for the sake of sim- 
plicity, by assuming a mean coefficient c p so that 

h l+ h s , V2 

= c 1 _J> (9* 
d 2g 



J, 



there results 

/ P p w 

-fhihU 1 w _^log _J_4-_^/ p.-p 

V IT s; ^ w , w a u e p u v 1 



V2_ V 2 , V 2 

b i . ' 1 b 

—55- D_r ^ (10> ' 

Adding this equation to (4) gives 



l b log P '- P »- P » 
e 



W _|_W u " p u 

a 1 w \ b b w 

h 1 +^( 1 + C pX) + 5 C e W 



2g \ w <* / 2g 

Neglecting the second term on the left hand side of the equa- 
tion, which will be very small in comparison with the first term 
on account of the large difference between the values of u w and 
u b , w a and w w , and neglecting w a in the denominator, this equa- 
tion reduces to the simple form 

Wp p. v2 / \ V.2 

w u e p ^ 2g ^ » d p 2g e U ' 

w b b \ / 

In developing this energy equation Dr. Lorenz assumed the 
velocity of air entering the foot-piece as equal to that of the 
water ; that is free from any losses due to impact which may be 
readily assumed on account of the small kinetic energy of the 
air. 

Now let 

p p. 

1 w a — log _1 ' (13) 
i a u e p 

b *b 

the work of isothermal expansion of the weight of air w a , and 

[431] 



28 BULLETIN OF THE UNIVERSITY OP WISCONSIN 

1 — w w hi the work done in lifting the fluid weight w w , from 
which the hydraulic efficiency 

1 w h u 

° w 1 b ... ... 

e=— = (14) 

I P. 
1 w p log — L 
a 1 b G e p 

can be computed with the aid of equation (12) 

v2/i+ c J_\j_ V2 c 

— =1 -f — (15) 

e 2gh ' 

* 1 

For the practical use of these formulas it will be better to 
eliminate the velocities v b and v i? by introducing the volumes 
•q b and q w of weights w a and w w and using the area of the dis- 
charge pipe a p , by means of the following formulas : 



q. u w — q u 

b b www 



q 4_ q — a v q — a v 

b 1 w p b w pi 



"Writing now in place of equation (12) 

^ip g jLi = h + f (j+ °pj) ( q b + 

Q u e p^ 1 \ 2 s a2 

WW b \ » n 



w / i e w 



(16) 



(17) 



p 

-and differentiating this equation with respect to q b , putting 

d q 

w = o, 



d q 



there results as a requirement for maximum discharge q^ 



i p h v. i + c _L 

_L_L J log _L = _ g d 
w w ^b 8 a~ 



( q b+ q w) ( 18 ) 



or in connection with equation (17), that is after eliminating 
the pressures pi and p b , 

( 1+ C pl)( q b- q w)= 2gh 1 a p 2 + C e^ 

If now the maximum discharge determined from the capacity 
of the well, and the area a p of the discharge pipe determined 
from the diameter of the well, and also the lift and the known 
^coefficients c e and c p are given, the volume of free air required 
may be computed by means of the formulas (18) and (19) from 

[432] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



29' 



which the submergence h s can then be computed by means of 
equation (4). For these fixed conditions equation (17) then 
gives the relations between any desired values of q b and q w 
using the same pressure pi. 

There may be other losses of energy than those accounted for 
by Dr. Lorenz, such as the loss due to the elbow or bend which 
generally forms the upper end of the pump. In comparing the 
experimental results of the Wisconsin experiments with Dr. 
Lorenz 's theory (see page 77), his formulas have been modified 
to take account of the elbow loss, and in computing experi- 
mental values of the coefficient of pipe friction and slip, a term 
has been introduced to correct for the loss of energy due to 
friction in the air pipe (see page 73). 

Green's Theory. — In the Engineering and Mining Journal of 
Aug. 7, 1909 (Vol. 88, p. 251), Leonard M. Green has published 
an article entitled "Efficiency of the Air Lift as a Solution 
Pump/' in which he discusses mathematically the theory of the 
air lift, amount of air required, minimum air pressure, effi- 
ciency of the lift under given conditions, etc. 

He makes the assumption that the water and air rising in 
the eduction pipe are in layers; the layers of water being 
equal in volume and the layers of air being of equal weight. 
Formulas are deduced for computing the ratio of the volumes 
of water and free air in each layer for given conditions of lift 
and submergence and for giving the number of these layers, 
or the volumes of water and air discharged. 

No provision is made in the formulas for correcting for 
entrance loss or for the loss caused by the elbow, at the top 
of the eduction pipe, which may amount to as much as 15 per 
cent, of the total work done. Nor has any account been taken 
of the slip. An attempt has been made to correct for pipe 
friction by assuming that the velocity in the tail-piece of the 
eduction pipe is equal to the velocity of flow of water in a 
clean iron pipe of length equal to that of the eduction pipe and 
under a difference of head equal to that caused by the com- 
pressed air. The experiments made by the writers indicate 
that this last assumption may be approximately true for some 
ratios of volume of air to volume of water, but that it is very 
far from the truth when this ratio is small. 

[433] 



80 BULLETIN OF THE UNIVERSITY OP WISCONSIN 

By neglecting the entrance and elbow losses and making the 
above assumption as to pipe friction the author computes the- 
oretical efficiencies of more than 90 per cent, for small amounts 
of air, and draws the conclusion that under proper working 
conditions the total combined efficiency of the compressor and 
lift should not be less than 70 per cent. Experiments do not 
justify this opinion. 

The Green formulas are not so convenient for use as the 
Lorenz formulas, so no attempt has been made by the writers 
to supply the missing terms or to work out experimental co- 
efficients for use with them. 



[434] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



31 



METHOD OF OPERATION 

To start the operation of an air lift pump requires a greater 
air pressure than is necessary for normal operating conditions. 
When the air supply is first turned on, the air pressure must 
be greater than that due to the submergence of the air inlet, 
while after the discharge of the liquid from the pump has com- 
menced the pressure at the air inlet will be reduced by the 
amount of the entrance and velocity heads of the liquid enter- 
ing the eduction pipe. The conditions existing while starting 
an air lift pump are accurately illustrated and described above 
in connection with Fig. 2 (a) with the exception that instead 
of only one bubble of air there would be many. When a suf- 
ficient number of bubbles have been introduced to raise the 
head through the entire lift, some of the liquid will begin to 
spill out over the top of the pipe. The loss of this liquid causes 
a reduction in the pressure in the eduction pipe, which under 
some conditions allows a sudden influx of the high pressure 
air, resulting in a violent discharge of liquid and air which 
may exhaust the store of compressed air. Following this the 
liquid would regain its full static head, requiring the operation 
to be started over again. 

To prevent such intermittent action the escape of air into 
the eduction pipe must be controlled. It should be throttled 
the instant the discharge of liquid commences. That intermit- 
tent action does not always occur is probably due to the effect 
of friction in the air pipe. As this friction increases with the 
square of the velocity, it is evident that in long pipes of small 
cross-section it will serve to some extent as a governor, tending 
to control the discharge of air. 



[435] 



32 



BULLETIN OF THE UNIVERSITY OP WISCONSIN 



DESCRIPTION OF AN AIR LIFT PUMPING PLANT 
The Pump 

The essential structural features of the air lift pump are ex- 
ceptionally simple and few in number, and this fact constitutes 
one of its principal advantages. In its simplest form, as illus- 
trated in Fig. 3, it consists of a pipe for the discharge of the 
water and a smaller pipe for conveying compressed air to it 
at a point near its lower end. 

The Eduction Pipe. — The discharge pipe is designated by va- 
rious writers as the eduction pipe, lift tube, lift pipe, and rising 
main. It should not touch the bottom of the well or reservoir 
from which it is to pump but should be elevated above it so as 
to freely admit the water or other liquid through its lower open 
end. This end of the pipe should, however, be submerged be- 
low the liquid surface a distance which, our experiments indi- 
cate, should be greater than the height above the water sur- 
face to which the liquid is to be lifted. This latter distance 
is technically called the lift of the pump. The distance meas- 
ured from the water surface down to the point of admission 
of the air into the eduction pipe is known as the submergence 
of the pump. Submergence is generally expressed as a per- 
centage of the total length of the pump, measured from the 
point of air inlet to the point of discharge. The discharge 
should be free into a reservoir at atmospheric pressure. Sub- 
mergence and lift should be measured from the elevation of the 
water as it stands under working conditions rather than under 
static conditions. 

The Foot-Piece. — In most air lift pumps the compressed air 
from the air pipe enters the eduction pipe through a casting 
designed to cause the air to enter in a special manner. The 
casting used for such a purpose is technically called a foot- 
piece. 

The type of foot-piece devised by Mr. Frizell is shown in 
Fig. 4. In the specifications for his patent it is described as 
follows : 



[436] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



33 



' 'Into the bottom of the rising-pipe is fitted the hour-glass- 
shaped pipe 5, inclosing between the two pipes the annular 
space E E. 

"The upper end of the pipe 5 is perforated with a great 
number of minute orifices, F, as indicated by the black dots. 




Fig. 4.— Frizell's Foot-Piece. Fig. 5.— Pohle's Foot-Piece. 



The lower end expands to a greater width than that of the 
rising-pipe in order to diminish the resistance of the water in 
entering. 

"The pipe D, leading from the source of compressed air 
opens into the annular space E E. 

"The pipe D, which conveys the compressed air may pass 
down in the pit C, as shown, or inside the rising-pipe B, or out- 
side the pit C in the ground, if preferred." 

Dr. Pohle's foot-piece is illustrated in Fig. 5. The descrip- 
tion of it, taken from the specifications for his patent, is as 
follows : 

"The exit end of the air pipe is enlarged by beveling off the 
inner edge thereof, in order to permit the free delivery of the 
air in mass or bulk, and thus to avoid the formation of air bub- 
bles. The enlargement C of the pipe W is of sufficient area to 
compensate for the space occupied by the exit end of the air 
pipe A, and said end of said pipe A passes through the vertical 
side of the enlargement C, as shown, and derives support there- 
from. ' ' 

Quite a large number of different foot-pieces have been de% 
\ised and patented and in most cases extravagant claims have 
been made for them as regards their effect in increasing the 

3 [437] 



34 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

efficiency of the pump. A few of the types will be illustrated 
and discussed on a following page, in connection with the de- 
scription of the experiments carried on at the Hydraulic Labora- 
tory of the University of Wisconsin. 

As will be shown later, experiments indicate that changes 
in the form of the foot-piece have little if any effect on tlje 
efficiency and capacity of the pump, other than the effect due 
to the amount of obstruction of the water passages; a factor 
which differs in the various types. 

Tail-Piece. — Most forms of foot-piece are arranged for the 
attachment of a pipe onto their lower ends, thus extending the 
eduction pipe some distance below the point of air admission, 
for the purpose of preventing the escape of compressed air 
from the bottom of the eduction pipe. The pipe used for such 
an extension is termed a tail-piece. The tail-piece is often 
made a larger size of pipe than is the remainder of the educ- 
tion pipe. The length and size to be used for a tail-piece are 
problematical. 

A number of distinct types of air lift pump have been pro- 
duced through the various methods that have been devised for 
piping the w^ells. The methods in most frequent use are illus- 
trated in Figs. 6 and 7 and are described below. 

Side Inlei Pump* — The side inlet pump, in which the air pipe 
is on the outside of the discharge pipe, is shown, at (a) in Fig. 
6. The air pipe is connected to the bottom of the eduction pipe » 
by means of standard fittings, special castings, or one of the 
various patented foot-pieces, examples of which are illustrated 
in Figs. 11 and 12. This method is used when the well is large 
enough to admit of the air and water pipes being placed side by 
side from top to bottom and is probably the most economical 
of the systems shown. 

Annular Air Tube Pump. — Fig. 6 (b) shows the annular air 
tube pump in which the well top is sealed and the air passes 
down through the annular space between the discharge pipe and t 
the air pipe or well casing. 

In the illustration accompanying the 1865 patent of A. 
Brear's annular tube pump, a foot-piece is shown attached to 
the lower ends of the eduction and air pipes. This nozzle is so 



[438] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



35 



arranged that the air is directed upward into the center of the 
eduction pipe, the liquid entering the lower part of the foot- 
piece and surrounding the air nozzle. The air is introduced 
differently in the Bacon pump, which has been quite extensively 




la) (b) *(c) fd) 

Pig. 6— Different Methods of Piping Wells. 

used. In the original patent (No. 542,620) of James E. Bacon, 
issued July 16, 1895, the statement is made that it was found 
" advantageous to make an opening into the uptake-pipe near 
the bottom end thereof, so that the air may flow through that 
opening in a uniform or nearly uniform stream. " Many annu- 
lar tube pumps have been built with no foot-piece or opening 
in the side of the pipe. In such pumps the air forces the water 
level in the well down until the bottom of the discharge pipe 
is uncovered. Air then enters the discharge pipe and the press- 
ure in the annular space is lowered. This causes the fluid to 
rise again in the air space and discharge pipe until the pres- 
sures balance and then the operation is repeated. This causes 
the water in the well approaching the bottom of the eduction 
pipe to surge more violently than it would if it were allowed 
to rise in the well around the eduction pipe to its normal 
height, as it does in the side inlet system. It is claimed for 



[439] 



36 BULLETIN OP THE UNIVERSITY OF WISCONSIN 

pumps built in this way that this surging promotes the en- 
trance of the water and air into the eduction pipe in a manner 
conducive of high efficiency. 

Central Air Tube Pump. — Fig. 6 (c) shows the central air 
tube pump which uses the well casing as the discharge pipe, 
and introduces the air through a small pipe usually fitted with 
some special device or foot-piece attached to the bottom 
through which the air escapes. Usually a number of small holes 
are drilled, or a number of slits cut into the lower joint of pipe 
and the end plugged. An objection to this method is that when 
the well is cased for only a portion of the distance, the air and 
water may escape out of the well into fissures in the rock. The 
hydraulic radius of the water passage in the discharge pipe 
is reduced by the air pipe, which increases the frictional losses 
and so diminishes the efficiency, but in this method of piping 
the entire cross-section of the well, less the area of the air pipe, 
is available for use as a discharge pipe ; so a well piped in this 
way will have a greater theoretical capacity than wells of the 
same size piped by the other methods ; notwithstanding the 
obstruction caused by the central air pipe. This fact is shown 
by the following comparison of the three methods. Assum- 
ing in each case that the wells are of 6 inches diameter, the 
largest eduction pipe w T hich can be got into the well with a 
1-inch air pipe beside it, is 3Vo inches in diameter, while in the 
annular tube method of piping a 4 1 / ^-inch eduction pipe can be 
accommodated. In the central tube system it is assumed that a 
lV2-nich air pipe is used with the 6-inch casing serving as the 
eduction pipe. The tabulated values of the areas and perimeters 
of the pipes were taken from the table of standard dimensions 
of wrought iron and steel pipe published in the Crane Com- 
pany's catalogue. It may be noted in the following tabulation 
that the hydraulic radius of the central air tube pump is less 
than that of the annular tube pump, but the net area of the 
former is nearly tAvice as large as that of the latter. The dis- 
charge through a pipe under a given head is proportional to 
the product of the area and the square root of the hydraulic 
radius of the pipe. This product has been calculated and tabu- 
lated in the last column and shows the relative capacities of 
the wells piped according to the three different methods, as- 

[440] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 37 

suming the value of the coefficient of pipe friction and slip to 
be the same in all three cases. 





Nominal 
Size 
of 
Well, in 
Inches. 


Nominal 
Size 
of 
Educ- 
tion 
Pipe, in 
Inches. 


Nominal 
Size 
of 
Aii- 
Pipe. in 
Inches. 


Approx- 
imate 
Net Area 
of Educ- 
tion 
1 ipe. in 
Square 
Inches. 


Approx- 
imate 
Wetted 
Perime- 
ter, in 
Inches. 


Hydrau- 
lic 
Radius, 

in 
Inches. 


Dis- 
ch arg'e 
Func- 
tion. 


Side Inlet 
Pump 

Annular Tube 
Pump 

Central Air Tube 


6 
6 
6 


34 
44 
6 


1 

6 

14 


a 

p 

9.89 
15.96 
26.05 


11.15 
14 62 
25.02 


r 

0.89 

1.13 
1.04 


a sir 
P 

9.33; 
16.9, 
26. 5 



Combination Pump. — Fig. 6 (d) shows a combination of the 
annular air tube and central air tube methods of piping. It 
is evident that the hydrostatic head in the well cannot be 
greater than that due to the ground water to permit of con- 
tinuous operation. Therefore, no special advantage is to be 
gained in introducing compressed air above the w T ater surface 
in the well, unless the increased surging, due to the less depth 
of water on the outside of the eduction pipe, might effect the 
size of bubbles of air admitted. The results of the authors' ex- 
periments show, that with the well piped according to the side 
inlet method using a Harris Air Pump Company's foot-piece, 
there was no appreciable difference when compressed air was 
introduced above the water surface in the well and when the 
well was open to atmospheric pressure, the percentage of sub- 
mergence and lift being the same in both cases. The cut shows 
this system with a patented foot-piece on the end of the air- 
pipe. 

Multiple Air Lift Pump. — When the lift is very high and the 
proper submergence difficult to obtain, the arrangement shown 
in Fig. 7 may be used where the cross-section of the well per- 
mits of its use. This arrangement employs a series of suc- 
cessive lifts and it is claimed that it works more economically 
than when the water is raised in a single lift. The cross-sec- 

[441] 



38 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



tional area of the ordinary deep well will not permit of such an 
arrangement, but it may be used to advantage in a mine shaft. 




t 



Fig. 7.— Multiple Air Lift. Fig. 8— Air Separator. 



Return Air Pump. — In rising through the eduction pipe there 
is a transfer of heat between the air and the water; the tempera- 
ture of the two being practically equal at the point of discharge. 
Therefore, where the air lift is being used to pump from under- 
ground supplies, the temperature of the air issuing from the 
discharge pipe will be cooler than the atmosphere during the 
warm months of the year. For each five degrees fall in the 
temperature of the free air entering the compressor, a saving of 
about one per cent, in the expenditure of energy used in doing 
the work of compression may be effected. Hence, where the 
wells are situated in close proximity to the power house, con- 
siderable economy may be effected by connecting the air inlet 
of the air cylinder of the compressor with the top of the well 
casing head. An air separator used for this purpose consists 
of a cylindrical drum about 18 inches in diameter and 8 or 10 

[442] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 39 

feet long, attached to the casing head from the side of which 
the discharge from the well passes out and from the top the 
air is piped to the compressor, An air separator is shown in 
Fig. 8. The return-air method of piping may be used with any 
of the types of pumps shown in Figs. 6 and 7. 




Fig. 9.— Air Lift Pumping Plant. 



The air separator described above is useful also where it is 
desired to pump to points situated some distance from the 
well, as described on page 42. 

Diverging Outlet Pump. — When the eduction pipe is of uni- 
form diameter throughout, as shown in Figs. 3, 6, 7 and 9, the 
discharge occurs at quite high velocity, resulting in a con- 
siderable loss of energy. To conserve this kinetic energy of 
the water Mr. Jos. Price, an English engineer, fitted his pump 
with an eduction pipe which increased in diameter towards the 
top, so that as the compressed air expanded in rising the 
velocity would not be greatly increased. This device could be 
used with any type of foot-piece and any method of piping. 
A few experiments by the authors indicate that a considerable 
saving may be effected by the use of a diverging outlet of 
proper design. 

[443] 



40 



BULLETIN OP THE UNIVERSITY OF WISCONSIN 



The Plant 

An air lift pumping plant comprises the motive power, an 
air compressor, an air receiver, and an air pipe leading to one 
or more pumps such as have been described in the preceding 
paragraphs. Fig. 9 serves to illustrate in a general way the 
machinery and other essential apparatus. 

The compressor and receiver should be located where the ex- 
pense of installing and operating the plant will be the least. 
They are often situated a considerable distance from the wells. 
The power used to drive the compressor may be either steam, 
electric, water, or internal combustion engines. 

The Compressor. — The type of compressor installed will de- 
pend on the pressure required to pump the wells, the nature 
and amount of power available for compressing the air, and 
the number and size of the wells. "Where the pressure required 
is small and the quantity to be compressed not very large, the 
ordinary straight line or duplex compressor may be used. 
Where high air pressures are necessary economy demands the 
cross compound type fitted with an intercooler. 

The Receiver. — The receiver is used to store and equalize the 
air pressure. It acts in much the same way as the air cham- 
ber on a force main and reduces the effects of the pulsations 
of the compressor. It also acts as a separator to catch the 
water and oil which are carried by the air. It is quite necessary 
to provide some kind of a separator for this purpose to prevent 
the air pipes becoming clogged, and where a foot-piece with 
small air openings is used it is especially desirable to have the 
air free from any clogging material. The air receiver is 
usually built of boiler iron and designed so as to permit a 
steady now of air to the well. The air from the compressor 
passes down from the top of the receiver through a pipe and 
discharges beneath the surface of some water which is usually 
kept in it. The outlet pipe for the air is located near the top 
of the receiver, and a drain is provided at the bottom to carry 
away the oil and water. 

The Air Line. — From the receiver the main air line runs to 
the wells. The piping to the wells should be arranged to avoid 



[444] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



41 



unnecessary valves, elbows and bends, as these reduce the effi- 
ciency of the plant. The same precaution should also be taken 
in the design of the water pipes. A valve should be placed on 
the air main in the power house so that the wells may be con- 
trolled from a central point. It is desirable to place a regulat- 
ing and a stop valve at each well so that after the proper 
amount of air has been adjusted to the conditions of lift, sub- 
mergence, etc., at the well, it will not be necessary to disturb 
the adjustment in order to shut down the well. 

In the following pages the discussion will be confined to the- 
air lift pump alone, leaving out of consideration the efficiency 
of the air transmission pipes, compressors and other appurte- 
nances, which have an important bearing on the desirability 
of installing air lift pumping plants, but the consideration of 
which is beyond the scope planned for this bulletin. 



[445] 



42 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



DISADVANTAGES OF THE AIR LIFT PUMP 

The air lift pump, in common with every other device, has a 
number of disadvantages, the principal ones being its low effi- 
ciency, the great depth of submergence required and its poor 
adaptability to conditions requiring the discharge to be con- 
veyed great horizontal distances. 

Low Efficiency. — The most serious of the above mentioned 
disadvantages is the low hydraulic efficiency of the pump. The 
pump is generally credited with efficiencies of only 25 to 33 
per cent, but notwithstanding the low efficiency of the pump 
itself, the entire air lift pumping plant in some cases develops 
a duty which compares favorably with other systems of pump- 
ing. 

Great Depth of Submergence. — A single air lift pump cannot 
be used in a shallow well or reservoir except to raise the liquid 
a very small distance, owing to the high percentage of the total 
length of the pump which must be submerged to give good 
efficiencies. This fact limits the field of the air lift pump prin- 
cipally to deep well pumping. The multiple stage pump de- 
scribed on page 37 overcomes the difficulty, but probably at the 
cost of reduced efficiency. 

Limited Horizontal Pumping. — Several plants have been in- 
stalled where the air lift w T as used to pump the water a con- 
siderable horizontal distance after it had been raised to the 
surface of the ground, but such plants are not considered effi- 
cient. The air in passing through the horizontal or even an 
inclined pipe, is not likely to be evenly distributed throughout 
the cross-section of the pipe, but is likely to pass along under 
the upper side, allowing a large space in the lower portion of 
the pipe for the water to slip back past the bubble. In a hori- 
zontal pipe the air cannot exert any buoyant effort to aid in 
discharging the water, and its expansive force, which might 
be used in overcoming pipe friction is not likely to be effective 
on account of the serious amount of slip which occurs under 
these conditions. "Where it is desired to convey the water to 
a point distant horizontally from the well, the eduction pipe 

* [446] 



DAVIS & WEIDNER— THE UR LIFT PUMP 



43 



should be carried vertically above the well a height equal to 
the friction head of the water in the horizontal conductor, and 
at its top it should be fitted with an air separator, such as the 
one described on page 39. From the separator the water w T ould 
flow by gravity to the desired point. 

Aeration. — The thorough aeration of the water pumped is 
generally regarded as an advantage, but under some circum- 
stances it is a disadvantage. It doubtless promotes the rust- 
ing and consequent destruction of the eduction pipe and in 
some cases causes a deposit of salts which clogs the water pass- 
ages, especially in the foot-piece. The opinion has also been 
expressed that compressed air causes an excessive growth of 
algae. The bacterial content of water is somewhat increased 
by the air lift unless the air supply is filtered. 



[447] 



44 



BULLETIN OF THE UNIVERSITY OE WISCONSIN 



ADVANTAGES OF THE AIR LIFT PUMP 

The air lift pump possesses many features which give it de- 
cided advantages over other types of pumps, when applied to 
certain conditions. 

Large Capacity. — Its principal claim to superiority lies in its 
large capacity. "When the conditions are suitable for its in- 
stallation, an air lift pump will discharge more liquid from a 
well of small bore than will any other type of pump. This is 
due to the fact that almost the entire cross-sectional area of 
the well is available for the flow of liquid and the action is 
nearly continuous. The quantity that can be discharged by 
an air lift pump is only limited by the capacity of the w T ell and 
the expense of pumping at unreasonably high rates ; while 
deep well pumps, the majority of which are single acting, limit 
the discharge by the allowable piston speed, which usually 
does not exceed 100 feet per minute. The air lift affords a 
ready means for testing the capacity of a well even if it is not 
to be permanently installed. 

Low Maintenance Cost. — Owing to the simplicity of the pump 
the expense of maintenance of the plant is very low, and is due 
principally to the expenses in connection with the compressor. 
The operation of the air lift is exceedingly simple and the life 
of the pump is almost indefinite. Sometimes the air pipes and 
foot-piece become clogged with the oil carried over from the 
compressor cylinders and in that case have to be removed and 
cleaned, but this rarely occurs, and when it does the cost is 
small compared with the cost of replacing a mechanical pump. 
The fact that there are absolutely no moving parts in the well 
makes the pump especially fitted for handling dirty or gritty 
water, sewage, mine water and acid or alkaline solutions in 
chemical or metallurgical works, or other corrosive liquids. 
Mechanical pumps suffer from fine sand in the water, which 
cuts the packing, plungers, and valves in a short time and 
makes frequent repairs necessary. To repair such pumps they 
have to be stopped for a period of several days, resulting in a 
consequent waste of time and increase in expenses. Liquids 

[448] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



45 



that attack metals such as brine, sulphuric acid, etc. may be 
pumped by the air lift pump, because the pump and appurte- 
nances may be replaced at a small expense and loss of time. 
The application of the air lift as a dredge pump has been tried 
and found successful, but it has not been extensively used for 
this purpose. 

Low Operating Cost. — In places where the wells are scattered 
over a considerable area, or are remote from the power house, 
the air lift pump has an advantage over the steam driven pump. 
In a deep well pump driven by steam each well must be 
equipped with a separate engine and working barrel, which 
entails heavy condensation losses through long steam supply 
pipes. The expense of attendance of a plant of this sort with 
its scattered pumping units is great. In the air lift pump the 
transmission loss is much smaller and as no attendance at the 
well is required, they may be put in operation or controlled 
by a valve in the power house. 

Not Affected by High Temperatures. — Fluids of different den- 
sities and temperatures may be handled to advantage by the 
air lift in cases where the use of other types of pumps would be 
prohibited. In the case of a hot liquid the air absorbs part of 
the heat of the liquid and hence is increased in volume, so that 
the discharge of liquid for the same expenditure of free air is 
greater with hot than with cold liquids. This results in a con- 
siderable gain in efficiency for the pump. 

Aeration, — Where the water is to be used for a domestic sup- 
ply and there are impurities in it such as iron, it has been 
noticed that the iron is oxidized by the aeration of the water 
and the supply is thereby improved. Aeration is especially 
advantageous in the pumping of sewage on account of the aid 
it gives in the oxidation of the impurities. 

Reliability. — Air lift pumps are not liable to sudden stoppages 
or breakdowns. 



[449] 



WISCONSIN EXPERIMENTS 



The experiments made by the writers at the Hydraulic Lab- 
oratory of the University of Wisconsin, were begun during the 
summer of 1908 and were continued at various times there- 
after with modifications in the apparatus. 

Notation 

The notation and definitions used in the following discussion 
are given below: 

" Reading " is the term used to designate a single value ob- 
tained by the inspection of the scale of an instrument. 

"Run'' is used to designate such a combination of readings, 
made under practically constant conditions, as form a com- 
plete unit in the result. 

"Series" is used to designate those runs made with varying 
rates of pumping but with constant conditions of apparatus. 



[451] 



48 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



DESCRIPTION OF APPARATUS— 1908 EXPERIMENTS 

The 1908 experiments, comprising runs 1 to 318, inclusive, 
were made with the apparatus arranged as shown diagrammati- 
cally in Fig. 10. 

Eduction Pipe. — In this series of experiments the eduction 
pipe, which consisted largely of l^-inch glass tubing supported 
by a slotted 2-inch iron pipe, was exposed to view, thus afford- 
ing opportunity to observe the air and water rising in the pipe. 
The upper end of the glass pipe was coupled to a 1%-inch iron 
pipe, about a foot long, on the upper end of which was a cast 
iron elbow fitted with a nipple 2 inches long. A piece of canvas 
fastened to this nipple deflected the spray downward into a 
4-inch galvanized spout. This arrangement provided a free 
discharge into the air at the elevation of the elbow. 

Foot-Piece. — The foot-piece used in the 1908 experiments was 
a No. 2 Harris air pump* having a l^-inch discharge, a l 1 /*?- 
inch suction, and i/^-inch air pipe. A sectional view of the foot- 
piece used is shown in Fig. 11 (a) and an exterior view in 
Fig. 12. 

The Harris pump, as described in patent No. 814, 601, con- 
sists essentially of an ejector having a contracted passageway 
formed by a sleeve snugly fitted into its upper end, and having 
immediately below the sleeve a nozzle screwed into an air pipe. 
The walls of the ejector are enlarged about the air tube so that 
the dimensions of the passageway through the ejector are sub- 
stantially uniform. The air nozzle in the ejector differs from 
the form described in the above patent, in having the air dis- 
charge into the body of the ejector through a circular slot in 
the end of the nozzle, instead of from an open diverging tube. 
The sleeve and nozzle are shown in their relative positions in 
Fig. 12. 

Tail-Piece. — As used in the 1908 experiments the foot-pie^e 
was connected by a short nipple to a reducing flange on the 
top of a 6-inch flanged cast iron tee. This arrangement made 



* Made by the Harris Air Pump Co., Indianapolis, Ind. 

[452] 




[454] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



51 




Fig-. 12. — Foot-Pieces Used in Wisconsin Experiments. 

[455] 



52 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

the entrance to the pump approximately one foot below the air 
inlet. 

Water Supply. — The water supply, controlled by a 1-inch 
valve, entered the tee through the branch, the water passing 
through a 2-inch cross in which was inserted an iron ther- 
mometer well. The bulb of the thermometer in the well was sur- 
rounded by mercury in order to make the thermometer respond 
quickly to changes in the temperature of the water. 

For the purpose of determining the head of water at the 
air inlet, a %-inch nipple was tapped into the top of the 6-inch 
tee and was connected by means of a l^-inch glass tube, 
marked water gage in Fig. 10. A large glass tube was used 
in order to reduce the amplitude of the oscillations due to the 
variations of pressure caused by the surges of air in the educ- 
tion pipe. The head of water was varied during the experi- 
ments by adjusting the height of the outlet of the overflow hose. 
This overflow hose was quite necessary for the proper working 
of the pump as it served as a reservoir and standpipe, which 
regulated the flow of water to the well and kept the sub- 
mergence constant at different rates of pumping. The rate of 
pumping was determined by weighing, on a platform scale, the 
water discharged in a given interval of time. 

Air Supply. — The an' used in the experiments was drawn from 
one of the storage tanks of the University pneumatic pressure 
water works plant. This tank had a capacity of approximately 
3,000 cubic feet and was normally maintained at about 140 
pounds pressure, but during the air lift experiments the 
pressure was often reduced, owing to the use of the air, to the 
minimum under which the air lift would work. An automatic 
reducing regulating valve controlled the flow from the stor- 
age tank so as to maintain a practically uniform pressure in 
the receiving tank at the air orifice described below. 

The quantity of air supplied to the air lift was controlled 
by a valve in the ^-inch supply pipe near the foot-piece. The 
temperature of the air was measured by a mercury thermome- 
ter placed in a well similar to the one used to measure the 
temperature of the water. It was placed in a 2-inch tee on a 
branch leading from the main air pipe. A rubber tube, one 
end of which connected to the tee and the other end of which 

[456] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



53 



terminated in a glass tube, served to transmit the air pressure 
at the tee to the air space in the upper part of the lower 
bottle on a water gage. The pressure head in the air at the 
2-inch tee was indicated in feet of water by the difference 
of elevation between che water surfaces in the two bottles. A 
%-inch hole in the side of the upper bottle insured the pres- 
sure in this bottle being equal to that of the atmosphere. 
The two bottles were connected by rubber hose, the ends of 
which terminated in short glass tubes under the surface of the 
water in both bottles. As the pressure of the air used in the 




Thermometer We" O-^'-- fa f=>'—h Fi-o^r "A" 

Fig. 13.— Drum and Orifice for Air Measurement. 



different experiments varied, the height of one or both of the 
bottles was changed so as to prevent the surface of the water 
disappearing in the tube or overflowing through the vent hole. 
Bottles were used instead of glass tubes in this gage, in order 
to provide larger water surfaces, thus reducing the oscillations 
of the surfaces to one or two hundredths of a foot, instead of 
two feet or more which occurred when a tube was tried. 

Air Measurement. — To determine the quantity of air used in 
the experiments a standard sharp edged orifice, shown in Fig. 
13, was used. Its diameter was measured by a Starrett mi- 
crometer caliper reading to 1/1000 of an inch and was found 

[457] 



54 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

to be 0.480 inches. It was made of brass and was arranged 
to screw into an iron plate flush with its surface on the high 
pressure side. The iron orifice plate was bolted between two 
sections of 10-inch iron pipe. The air supply entered the longer 
section of 10-inch pipe through a 2-inch pipe. A Bourdon 
pressure gage connected to the drum was used to indicate the 
pressure in the drum while adjusting the pressure regulating 
valve. During the experiments the pressure in the high pressure 
side of the drum was more precisely determined by means of a 
mercury U tube gage, shown at A in Fig. 15, connected to the 
drum by a j4-inch iron pipe at a point 6 inches from the face of 
the orifice plate. During the 1908 experiments about 100 feet of 
%-inch pipe connected the orifice drum with the air lift pump. 
In Fig. 13, one of the thermometer wells, used for measuring 
the temperature of the air and of the water at the pump, is 
shown in detail. A mercurial thermometer placed in a similar 
well was used to determine the temperature of the air in the 
orifice drum. 

To measure the difference of head on the two sides of the 
orifice a bottle gage of special design, was connected to the 
orifice drum by ^-inch pipe at the points shown in Fig. 13. 
The bottle gage is shown in Figs. 14 and 15. It consisted of 
two inverted clear glass bottles about half filled with water 
and connected by a glass U tube, which passed through the 
stoppers but ended below the water surface. The air pressures 
on the two sides of the orifice were transmitted to the air 
spaces in the bottles by tubes which passed through the 
stoppers and ended above the water surface. When the press- 
ures were equal the water stood at the same level in both 
bottles, but when unequal the difference of pressure was bal- 
anced by the difference in the heights of the water surfaces. 
This difference in height was measured by means of two 
pointed brass rods which were coated with grease and slid 
through holes in the rubber stoppers. In use the two rods were 
raised or lowered by a small worm gear until their points were 
in the level water surfaces in the bottles, the relative elevations 
of the points being then determined by means of the scales 
and verniers attached to the rods and reading to 1/1000 of a 
foot. To get the actual difference of elevation of the points, 

[458] 



DAVIS & WETDNER— THE AIR LIFT PUMP 



55 




[459] 



56 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

or of the water surfaces, it was necessary to deduct from the 
difference indicated by the vernier readings a similiar difference 
indicated when the air pressure in the bottles was equal, as 
when the tubes were open to the atmosphere. The scale and 
vernier on the high pressure bottle were arranged to give read- 
ings increasing downward, while those on the low pressure 
bottle gave readings increasing upward. This arrangement 
made the computations easy, for in order to calculate the true 
difference of elevation of the water surfaces it was only neces- 
sary to subtract the sum of the initial or equal pressure vernier 
readings from the sum of the average vernier readings of any 
run. This arrangement of the verniers and scales also nulli- 
fied the effect of any leakage of water during an experiment, 
since a lowering of the water surfaces by leakage would in- 
crease the high pressure readings the same amount that it would 
decrease the low pressure readings, the sum of the two remain- 
ing the same. The leakage through the stoppers was very 
slight; not requiring replenishing in a year and a half. 



|460] 



DAVIS & WEIDXER— THE AIR LIFT PUMP 



57 



DESCRIPTION OF APPARATUS— 1909 EXPERIMENTS 

The 1909 experiments, comprising runs 319 to 608, inclusive,, 
were made with the purpose of determining the effect of varia- 
tions in the length of the eduction pipe, the form of the foot- 
piece, the presence of compressed air in the casing, and other 
features. These experiments required that the apparatus as 
originally set up be changed somewhat. 

The general arrangement of the apparatus as used in the 1909 
experiments is shown in Fig. 15. 

Well. — There was some doubt as to whether the arrangement,, 
used in the 1908 experiments, for introducing the water into 
the eduction pipe represented closely enough the working con- 
ditions of a pump in an actual well, and it was further desired 
to find the effect of compressed air outside of the eduction pipe. 
In the 1909 experiments the pump was, therefore, placed in a. 
well which consisted of a 6-inch wrought-iron pipe 22 feet long, 
capped at the top and flanged at the bottom to a 6-inch tee. 

Eduction Pipe. — The eduction pipe was the same as used in 
the 1908 experiments. The entire glass portion of the pipe 
with its supporting slotted 2-inch iron pipe was suspended in 
the well from the cap. During runs 319 to 379, inclusive, the 
length of the eduction pipe from the air inlet to the center of 
the elbow was 19.32 feet as in the previous experiments. Dur- 
ing runs 381 to 440, inclusive, the length was 26.74 feet, the 
increase being made by adding a length of 1% inch iron pipe 
above the well top. During runs 441 to 460 the length was 
41.50 feet, the addition being made as above. Runs 461 to 500" 
inclusive were made with different forms of foot-pieces which 
made slight variations in the length, 42.08 feet for runs 461^80 
and 41.6 feet for runs 481-500. 

Fool-Piece. — During runs 319 to 460, inclusive, the same Har- 
ris foot-piece was used as was used in the 1908 experiments. 
An Indiana foot-piece* was used during runs 461 to 480. It 
was a 1%-inch foot-piece reduced to l^-inch by a reducer at 



* Presented by the Indiana Air Pump Co., Indianapolis, Ind. 

[461] 



58 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

the top. During runs 481 to 500 the foot-piece used con- 
sisted of a common cast-iron reducing tee, the eduction pipe, 
tail-piece and air pipe entering the tee only so far as ah 
lowed by the standard threads on their ends, as shown in Fig. 
11 (c). The Harris foot-piece has already been described on 
page 48. The Indiana foot-piece was developed from the 
Harris foot-piece, the object, as stated in the patent specifica- 
tions, being to produce a simple, efficient, center-nozzle air lift. 
This foot-piece is shown in Figs. 11 (b) and 12, the various 
parts being indicated. In Fig. 12 the strainer has been removed 
to show the lower part of the nozzle, and the mixing tube or 
sleeve, into which the nozzle discharges the air, has also been 
removed and placed beside the foot-piece. The reducer can be 
seen at the upper end of the foot-piece. 

Tail-Piece. — In the 1S08 experiments the tail-piece was only 
about 2 inches long. Under the conditions of the apparatus 
used in these experiments, any air which may have escaped 
from the bottom of the eduction pipe into the 6-inch tee would 
have been carried into it again by the water. Under the con- 
ditions of the apparatus used in the 1909 experiments such 
would not have been the case. A tail-piece consisting of 1 foot 
of 1%-inch pipe was, therefore, screwed into the lower end of 
the Harris foot-piece, the length suitable for the conditions of 
our experiments having been determined by correspondence 
with the pump makers. The same piece of pipe was used as a 
tail-piece in connection with the tee used as a foot-piece in runs 
481 to 608. No tail-piece was used on the Indiana foot-piece. 

Water Supply. — "Water was introduced into the well by means 
of a 2-inch pipe connecting the branch of the 6-inch tee with the 
University main. The depth of the water in the well was regu- 
lated by means of a l^-inch overflow pipe connected at the 
lower end to the supply pipe and discharging at its upper end 
into the air. By varying the length of the overflow pipe any 
desired depth of submergence could be obtained. Provision 
was made, as in the 1908 experiments, for taking the tempera- 
ture of the water as it entered the well, by screwing a ther- 
mometer well into a 2-inch tee in line with the supply pipe. 
The water was discharged at the upper end of the eduction pipe 



[462] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



59 




[463] 



60 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

at atmospheric pressure into a conductor pipe, by means of 
which it was led to the weighing tank or discharged as waste. 

Air Supply. — The source of air and the apparatus for con- 
trolling it and for measuring it were the same as in the 1908 
experiments, but in the 1909 experiments the pump was set up 
only a few feet distant from the air measuring orifice. The air 
line was, therefore, shorter in these experiments. At the well 
the air line divided into two branches; one branch, marked 
pump air pipe in Fig. 15, supplying the pump through a %-ineli 
pipe, which entered the well through a stuffing box in the cap 
of the well, the other branch, marked casing air pipe, introduc- 
ing the air into the casing above the water in the well, through 
a %-inch pipe screwed into the cap of the well. 

Gages.— There were four gages used in making these experi- 
ments. The differential bottle, described in connection with 
the 1908 experiments, was used to determine the difference of 
head on the air orifice. The gage, marked A in Fig. 15, was a 
mercury U tube used for determining the head on the high 
pressure side of the orifice. Gage B measured the pressure at 
the bottom of the well, by means of which the equivalent sub- 
mergence could be calculated, when air pressure was exerted 
on top of the water in the well. The actual depth of water in 
the well was obtained by means of a glass gage attached to the 
outside of the well, from which the submergence could be di- 
rectly calculated when the water in the well was open to at- 
mospheric pressure. Mercury gage C measured the air pres- 
sure as it entered the pump, the valve in the pump air line 
being wide open. Air chambers were used on gages B and C 
to dampen the fluctuations of the gage readings, but this device 
was unnecessary as the readings were steady except when the 
water was so low in the well that air entered the pump through 
the tail-piece. The scales on the gages were made of steel, 
graduated to hundredths of a foot, and, by means of sliding 
verniers, readings could be obtained to 1/1000 of a foot. 

Leakage Tests. — All pipe joints and other places where an 
escape of air was possible were tested by applying soap solu- 
tion, which indicated small leaks by the formation of bubbles. 
The entire apparatus was made air-tight before any runs were 
made. [464] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



61 



METHODS OF OBSERVING 

Owing to the fact that different types of gages were used in 
the 1909 experiments than those used in the 1908 experiments 
for making some of the measurements, the arrangement of the 
data differed somewhat in the latter runs from the arrangement 
first used. The conditions of operation usually remained quite 
constant during a run, so that the gage and thermometer read- 
ings varied only slightly, if at all. Usually four or five read- 
ings of each instrument were made during a run, the length of 
a run varying from 3 to 15 minutes, and the discharge of water 
varying from 200 to 1,000 pounds. Time was measured by a 
calibrated stop-watch; temperatures were measured by mer- 
curial thermometers graduated to the centigrade scale and read- 
ing to tenths of a degree, and lengths were measured in feet. 

1908 Experiments. — Copies of the complete observed data of 
runs 30 and 132 are given below as samples to show the con- 



THE UNIVERSITY OF WISCONSIN. HYDRAULIC LABORATORY 
Experiment on H<?MS A/r Lift Put77p BMjUL NO...30 

Dat« by Mc Bride, Spr/ntzer, M///er, tDodcec»m V M^& by M///er t. Springe/? 

Date of Experiment Uu/f. /, J 90 8 cnecAed by - f. B. A/e/son 

General Data . Barometer * 29- 0/ ins. Mercury ._ 

Length of Pump.-? 19,32 fit. 5/x.e of Pump^/*"-- 

Zeros of Bott/e Gage. O. 22 9 +M.403. = 





Lift 
Minus 
3ft 


Dura- 
tion 
of 

Pun 


Water 




A/r 








We/ght 
in Pounds 


7~emp 
°C 


Temp 

at 
Pump 

°C 


Water Gage 
for Pressor* 
at Pi/mp 


Merc. Gage 
for Pressure 
at Orifice 


Bott/e Gage 
forDiffr/ead 
on Orifice 


Temp. 

at 
Or/f/ce 

°C 


/n/tio/ 


Ft/rat 


Lower 


Upper 


left 


Right 


left 


Riaht 


































8.36 


/0"6 S 


O 


400 


2/6 


23.3 


/S.32 


7. OS 


zees 


5.860 


0.270 


0.442 


24 & 








6.36 








2/6 


23.3 


Z5.32 


703 


2.8 83 


5.855 


0.270 


O. 442 


24B 








6.36 








2/6 


23.4 


/5.32 


703 


2.890 


5.850 


0270 


0442 


24 8 








e.36 








2/6 


23.4 


/3~32 


7.04 


2395 


5.843 


O Z69 


442 


24.8 








e.36 








2/6 


23.3 


/S-32 


7.04 


















e.36 

3.oo 


606 6 




400 


21.6 


23.3 


Z5.32 
7.03 


7.03 


Z.686 


$£53 
2868 


0.2698 


0.4 4 2C 
02698 


24.8 








//.36 


8.29 


Z.965 




0.7/ /8 
O 6320 
0798 



stancy of the conditions of operation and the method of making 
the observations. The scale by which data were obtained for 



[465] 



62 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

computing the lift and submergence was inverted and placed 
with its zero three feet below the center of the outlet of the 
pump. The readings of the scale, from its zero down to the 
water surface in the water gage (see Fig. 10), were, therefore, 
three feet less than the true lift. 

1909 Experiments. — The apparatus for the 1909 experiment* 
was so arranged that only two men were needed for conveniently 
making the observations; one man reading the gages while the 
other took the time of the run, read the thermometers, observed 
the depth of water in the well, and weighed the water. The 
gages were read as nearly simultaneously as possible, by first 
setting the verniers on all the different gages and afterwards 
taking the readings. About four accurate settings of the gages 
could be obtained in a ten minute run. The thermometers were 
read to a tenth of a degree centigrade and the temperature was 
obtained at least twice during a run; usually at the beginning 

THE UNIVERSITY OF WISCONSIN. HYDRAULIC LABORATORY 
Experiment on Marf'S A/f L/ft Pj/S7?0 ....... _ S.Mn...Mo^.J3Z 

d.i. hy. Mc BrJcfe t Springer, Mi/Jer.. t Dodge computed by Mi//er t. Springer - , 

Date of Experiment. - Uo/y 30, /908 checked 4j - £■ 3. Ne/son 

General Data 3 oromefer • 29.04 . Mercury -.. . , , 

«™ — „ L e/igth of Pump =. J9.32 S/z.e of Pomp =/Jfj/t. 

, Z eros of Bott/e Gage = 0.2 0.33/ = 0. 030 . . ... 





Lift 
M/nus 
3ft. 


OunJ 
. t/on 

Of 

Aon 


Water \ A/r 








Weight 
in Pounds 


Temp 

°C 


Temp 
of 

Pump 

°c 


Water Gage 
p or Pressure 


Merc Gage 
for Pressure 
or Or/ f ice 


3ott,'e6oae 
forD/fr/Teaa 
on Or/f/ce 


Temp. 

at 
Orif/ce 

°C 


l/t/tia/ 


F/nO/ 




Lower 


Upper 


£eff 




Left 




































Od7 




40 


440 


26 4 


25.6 


Z5.42 


0.44 


3./40 


559Z 


0.398 


0.428 


29.0 








08 7 








20.4 


258 


Z5.42 


044 


3/48 


5S97 


0397 


0.427 


29 O 








86 








26 4 


25.8 


/542 


45 


3./50 


5S03 


0.397 


0.427 


29.0 








086 








2 6. 4 


25. 8 


Z5.42 


045 


3./S4 


5 5 go 


0.396 


0.426 


29.0 








36 








26.4 


25.9 


/S.42 


0.45 


















0864 
3.0 OO 


20/ $ 




400 


26. 4 


25.8 


Z5.42 
045 


0.4S 


3/43 


5585 
3/48 


0.397 


0.427 
0.397 


Z9.0 








3.864 


M.97 


Z.437 


0.824 
p. 6*30 
0/94 



and end. The method of weighing the water was as follows: 
The empty tank weighed about 150 pounds, so a 200-pound 
weight was placed on the scale beam and the water diverted into 
the tank. When enough water had run into the tank to cause 
the scale beam to rise, a stop watch reading to l/ 5 of a second 



[466] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



63 



was started. Additional 100-pound weights were then placed 
on the scale beam and the watch was stopped when the beam 
rose again. The time and number of weights added while the 
watch was running were then recorded. The length of a run 
varied from 3 to 15 minutes depending on the depth of sub- 
mergence and the amount of air supplied to the pump. 

The readings for some of the runs were taken by a sin- 
gle observer, and it was not possible for one man to get more 
than two sets of gage readings during a run, the length of 
which was limited by the capacity of the measuring tank. It 
was entirely unnecessary to take more readings, because as a 
rule the readings were identical, and two readings of each in- 
strument served as a check to prevent blunders in observing 
and recording. The complete data of runs 338 and 482 are 
given below. 



"THE UNIVERSITY OF WISCONSIN, HYDRAULIC LABORATORY 

k^^.* Harris Air Lift Pump Run No. 338 

\>«»\>j„Weid/7er Gtocker - _ computed by We /drier 

Date ol Experiment A U£. /3 '.. /909- _ „ ChtCktd & ' £■ B. A/e/SO/7 

General Data Datum Re a din g on S ubmergetiee G oge = 3. 00 f t. 

L engths o f Pump = 19.32 ft - 

_ Barometer s 28. 95 Jns. Mercury ,. Z. eros of 3ott/e G a#es 

Z 0,3/3 £ J? 0.3/9 = 0.632 



Air Orifice 


Submer- 
gence 
Gage 


Air Goge 
at Pump 


Tem 


perature 


DeptA 
of 

Water 
in 

We//» 


Weight 

of 
Water 


Pi/ra- 
tion 
Of 

Run 




3ott/e 
Gage 


Mercury 

Gage 


Air 
at 

Qr/f/ce 


Water 
ot 

Pump 


/Air 
at 

Pump 


Left 


R.gfit 


Left Right 


Left 


Right 


left 


R/g/it 


In/trai 


F/nof 
































oz/o 


OZ// 


1.2/6 


3.637 


/./04 


2.4/6 


/096 


2.472 


27.3 


24.2 


2S.6 


/■6Z 


/go 


/0 90 


7~27~ 




0.2093 


02/0 


/2/e 


3.637 


/./04 


2 4/6 


/■096 


Z.472 


273 


24.2 


2S.6 


766 










0.2O9 


02/0 


/.z// 


3.640 


/■/04 


2.4/6 


7096 


Z.472 


2 7.3 


24.2 


237 


7.70 










0.2O9 


0.210 


/■2// 


3.640' 


/./04 


2.4/6 


A096 


2 A 72 








/. 70 










0.2O94 


O.Z/0 Z 


/Z/3 


3633 


/ /04 


2.4/6 


/■096 


2.472 


yzr 


^2 


2316 


A69 




900 


447* 






0.63ZO 
0.4/96 
OZIZ4 




/■Z/3 


'amp/ 


/./04 


f: air 


/.09€ 


273.0 


Z73. 


2730 












2.423 
* C 


/■3/Z 

*essec 


/.370 
■ afov 


30Q3 
e Y/a 


Z97.Z 
ter 


296.0 



The observed temperatures of the air and water at the en- 
trance to the pump were not used in the computations and 
hence are not tabulated in the final results of Table 1. 

Most of the computing was done with a Thatcher calculating 
instrument and all computations have been carefully checked. 



[467] 



64 



BULLETIN OP THE UNIVERSITY OP WISCONSIN 



THE UNIVERSITY OF WISCONSIN, HYDRAULIC LABORATORY 

Experiment 

Data \>y~*™*Jfltid/7en _„ Computed hr^We/dner^-^. 

Date of Experiment^/TgA- 2Z3 f ./S3>/0 - Cheeked 6 J - Ne/SOfl 

General Data: L e/ltfth^Of.. P(J/?7p~-., 4/- 6 ft, „„ 

O-Otum Reading.. O.a^J^M.bm.nr^eac.e. G age^ 6.67 ft. __ 

_ ....B arometec_-.29. 42. /ns. . Mercury „ 

„ ..Zeros „ of —,3oft/e ,. G ages 0. 2 99 ± 0.334 ' 0. 633 ....... 



Air Orifice 


Submer- 
gence 
Gage 


A'f Ga^e 
at Rc/rnp 


Te mperafvre 


PeptA 

of 
Wate/ 

vie// 


We/ffht 

of 
]/Vater 


Dora 
t/ot 
of 

Run 




3ott/e 
Gaffe 


Mercury 
Gaffe 


AJr 
at 

Onfici 


Water 

at 
Pi/snp 


Air 
at 


Left 


R,<;/rt 


Left 


Gyht 


Left 


f?,ght 


Left 


Q,0ht 


Inrt/Ol 


F/'na/ 


































0.24/ 


0.355 


0.790 




0.953 


2.673 


09/0 


3460 


I8.0 


77 


/83 


56 


20O 


/OOO 


5 "3 4 




0.24/ 


0.353 


0.7 90 


</./45 


O. 653 


2 673 


09/0 


54 BO 


179 


7.6 


/6.2 


5.6 












0. 633 




4/ 45 
0.790 




2 673 
653 




3.4 80 
09/0 


/7 9 
273.0 


7.0 
273.0 


/6.2 
273.0 


5.6 




800 


303*4 




O.S96> 
0.037 




3.335 


2.020 


2.570 


2909 


2€06 


289.2 



[468] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



65 



METHODS OF COMPUTING 

Quantity of Air. — The amount of air supplied to the pump 
was measured, as previously stated, by means of a circular ori- 
fice in a thin brass plate. The following formula derived by 
Mr. S. A. Moss* was used in computing the discharge through 
the orifice. 

in which 

q a = cubic feet of free air discharged per second. 

c = a coefficient of discharge. 

a 1 area of orifice, in square feet. 

p u = absolute pressure of air at upstream side of orifice, in 

pounds per square inch. 
p d = absolute pressure of air at downstream side of orifice, in 

pounds per square inch. 
T u = absolute temperature of air, in degrees Fahrenheit, at 

upstream side of orifice. 
The values of the coefficient of discharge were obtained from 
the curve shown in Fig. 16, in which the abscissas represent 
the difference in pressure in feet of water between the up and 
down stream sides of the orifice, and the ordinates represent the 
values of the coefficient of discharge for an orifice 0.48 inches 
in diameter. This curve was plotted from data published in 
an article "On the Measurement of Air Flowing into the At- 
mosphere through Circular Orifices in Thin Plates" by Mr. 
R. J. Durley.f 

Mr. Durley regards these data as being reliable to within less 
than one per cent. In view of this fact and the accuracy with 
which the temperature, diameter of orifice, and difference of 
pressure were measured, the writers believe the probable error 



* American Machinist, Volume 28, page 193, 1905. 

t Transactions Am. Soc. M. EL Vol. 27, page 193—1906. 

5 [469] 



66 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



should be within cue or two per cent, in measuring the quantity 
of air. 



.62 



o 

o BO 



.59 



.05 JO .15 .20 .25 .30 .55 
Di-f-ference in Feet of Water 
Tig. 16.— Coefficient of Discharge for Air Orifice. 



40 



.4 5 



.50 



The difference in pressure between the up and down stream 
sides of the orifice was measured in feet of water by means of 
the differential bottle gage shown in Figs. 14 and 15. p u was 
obtained by the following computation. 

(Reading of gage A in feet of mercury X 5.894) 

-j- (Barometer reading in inches of mercury X 0.4912) 
and pa by the following 

p u — (Bottle gage reading X .4333) 

The barometer readings were taken from the autographic 
record charts of the U. S. Weather Bureau. No correction to 
these readings was made for a standard temperature, as the 
difference in elevation between the Weather Bureau station and 
the Hydraulic Laboratory offset this small correction. 

T u being observed in degrees Centigrade a constant was in- 
troduced in the formula ; the diameter of the orifice being 0.04 
of a foot the formula then reduced to the following one 



C oX 3.6144^ 



PA 1 '"' 



\ 1 \ 1 




(21) 



[470] 



DAVIS & WEIDXER— THE AIR LIFT PUMP 



67 



The curve shown in Fig. 17 is plotted to give values of the con- 

P 

stant times the radical for different values of — ^ which values 

P„ 



P. 



multiplied by proper values of the coefficient c and 



1 T u 



give 



the discharge in cubic feet of free air per second. As an illus- 
tration, the computations for run 338, the data for which are 



1.0000 
.9998 
.9996 
.9994 
.9992 
.9990 











































> 


\ 
















































































































\ 


































































































































\ 













































































1.000 
.999 
.998 
.997 
.996 
.995 
.994 
.993 
.992 

.991 
.990 



.01 ,02 .03 .04 .05 .06 .07 .08 .09 JO .11 .12 .13 .14 .15 .16 .17 .18 

Values of 3.6I44V(^)^ [ffl™ 
Fig. 17.— Curve for Computing- Discharge of Air Through Orifice. 

given on page 63, will he used throughout the following dis- 
cussion. 

Average difference in pressure in feet of water = .2124 
p u = (2.425 X 5.894) + (28.95 X .4912) =28.512 
p d = 28.512— (.2124 X .4333) =28.4200 
T u = 300.3 
VT7= 17.329 
P.. 



1.6454 



i/T 
V u 



= 0.9967 



-3.6144 



V 



i) 



p 

I 

[471] 



=0.1112 (Curve Fig. 17) 



68 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



c = 0.6070 (Curve Fig. 16) 
q a = 1.6454 X 0.6070 X 0.1112 = .11108 
Theoretical Work Done by Air. — Assuming isothermal expan- 
sion of the air in its passage through the eduction pipe, — a very- 
reasonable assumption since the air absorbs heat from the 
water, — the mechanical work L done between the volumes q 2 and 
q lf is theoretically as follows* 



f f q ° 

=J Pdq = p 1 q 1 J 



dq 



PiQi log e ^ (22) 



The work done by one pound of air in expanding from an in- 
itial pressure p x to atmospheric pressure, (2116.8 pounds per 
square foot or 14.7 pounds per square inch) at 60° Fahrenheit, 
the standard temperature of the Moss formula, is : 
q 



L = p i q i log e- 



p q = p q 
i n *2 M 2 



p q 

q - 2 2 



P 2 q 2 log e |l (23 ) 



2 

The volume of one pound of air at 32° Fahrenheit and 14.7 
pounds per square inch pressure is 12.3880 cubic feet.t The 
volume of one pound of air at 60° Fahrenheit and 14.7 pounds 
per square inch pressure is, since 

P l q i P 2 q 2 



T T 

1 2 



14. 7 X 12.3880 _ 14.7 X q 2 
460 + 32 " 460+ 60 

% = 13.093 



* Carpenter's Experimental Engineering 6th Edition, p. 712. 
f Trautwine, pages 242 and 320. 



[472] 



DAVIS & WEIDNER 



—THE AIR LIi^T PUMP 



69 



The formula for L in foot pounds now becomes 



P. 



L = 14.7 X 144 X 13.093 X log 



e 14.7 X 144 



or using logarithms to the base 10, 



P. 



L = 14.7 X 144 X 13.093 X 2.30259 X log 



14.7 X 144 



P. 



L = 



63816.886 log 



(24) 



2116.8 



in which p x is expressed in pounds per square foot. The curve 
Pig. 18 was computed by means of this formula for different 
values of p x and was plotted to read pressures in pounds per 
square inch. In order to get the total work done, the value of 
work done in expanding from -p t to atmospheric pressure is 
added to the work done in expanding from atmospheric to baro- 
metric pressure, both values being obtained from the curve. 
In the 1908 experiments p x was measured by a water gage 
which gave the pressure in feet of water. In the 1909 experi- 
ments a mercury gage was used. 



Work done in expanding one pound of air from 22.330 pounds 
per square inch to 14.7 pounds per square inch == 11600 foot 
pounds (from curve). 

Work done in expanding one pound of air from 14.7 pounds 
per square inch to 14.22 pounds per square inch = 900 foot 
pounds (from curve). 

Total work = 11600 + 900 = 12500 foot pounds. 

Pounds of air used per second = .11108 X .076376 — .008481. 

Total work done by .008481 pounds of air in expanding from 
22.330 pounds per square inch to 14.22 pounds per square 
inch ■-= .008481 X 12500 = 106.02 foot pounds per second. 

Quantity of Water. — "Discharge of water in pounds per second 



n Discharge of water in cubic feet per second = 2.0135 X .0160 
= .03221. 

Discharge of water in U. S. gallons per minute = .03221 X 
7.48052 X 60 = 14.4580. 

[473] 



Pi 



= (1.376 X 5.894) + (28.95 X .4912) = 22.330 



900 



= 2.0135. 





70 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

Submergence. — The gage marked water gage in Fig. 10 meas- - 
ured the lift in the 1908 experiments, from which the percent- 
age of submergence was calculated by subtracting the lift from 
the total length of the pump and dividing the result by the 
total length. In the 1909 experiments the submergence was 
measured by the mercury gage B, Fig. 15. For runs 319-440, 
inclusive, the datum reading on the submergence gage was 



33 



3/ 



29 



.27 



25 



°- 23 

c 

























/ 






















/ 





































































































































































































21 



19 



/7 



J5 



13 



co o 
<o CO 
Q <o 
to 



O CO O 

o o o 

o o <0 

0Q CO c\j 



<o co 

<0 Q> 



o <o o 

co <o <o 

«0 CO CO 

CQ CO (\j 



Foot-Pounds of Work per Pound of Air 
Fig. 18.— Curve for Finding- Energy per Pound of Air at Various Pressures. 



+ 3.00 feet, while for runs 441-500 it was —6.67 feet. By 
datum reading on the submergence gage is meant the scale read- 
ing at the elevation of the air inlet of the pump. The follow- 
ing formula was used to calculate the percentage of submergence 
for the runs of the 1909 experiments. 

[ (Difference in feet of mercury, gage B, X 13.6) + (Left 
reading of gage B) —3.00 feet or + 6.67 feet] -j- Total length 
of pump in feet. 

[474] 



J** ' 



DAVIS & WEIDNER— THE AIR LIFT PUMP 71 

Percentage of submergence for run 338= 

(1.312 X 13.6) + 1.104 — 3.00 QO r f 
19^2 ~ 82 -° 4 

Lift. — Observed directly in 1908 experiments. In the 1909 
experiments computed from following formula : 

Lift=Total length of pump — (Percentage of submergence 
X total length of pump). 

Lift for run 388 = 19.32 — (82.51 X 19.32) = 3.375 feet. 

Actual Work Done in Lifting Water. — The product of the 
discharge in pounds per second and the actual lift in feet was 
taken as a measure of the actual work done. A few writers on 
the air lift pump have added the friction head in the eduction 
pipe to the actual lift, in computing the work done, but in the 
opinion of the writers the eduction pipe should be considered 
as a part of the pump. Actual work done in lifting water for 
run 338 = 2.0135 X 3.375 =s 6.7950 foot pounds. 

Efficii ncy — The efficiency of the pump was computed on the 
basis of the ratio of actual work done in lifting the water to the 
theoretical work inherent in the air, when expanding from the 
pressure at the gage to barometric prersure. By reference to 
Figs. 10 and 15 it will he seen that the gage pressure was 
measured within a few feet of the foo't-piece in the 1908 ex- 
periments, but that in the 1909 experiments the pressure was 
measured at a distance of 20 to 30 feet from the foot-piece in 
line with the air supply pipe. The efficiency, then, as computed 
is independent of the efficiency of the compressor and conveying 
air pipes to the well, but includes a short length of air pipe 
such as would be necessary to conduct the air from the top of 
the well to the foot-piece. The loss clue to friction in the air 
pipe and air nczzle is discussed on p. 73. Efficiency for run 

338= 6 .409 per cent. 

106.026 1 

I 

Ratio of Volume of Air to Volume of Water. — Obtained by 
dividing quantities in column 2 of Table I by quantities in 
column 6. ^Ratic of volume of air to volume of water for run 



338 = ill = 3 - 449 



[475] 



72 BULLETIN OF THE UNIVERSITY OP WISCONSIN 

Velocity of Water in a ly^-Inch Tail-Piece. — Obtained by 
dividing the discharge of water in cubic feet per second by the 
cross sectional area in square feet of a 114-inch pipe. Velocity 

for run 338 = — 3.779 f ee t per second. 



[476] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



73 



EXPERIMENTAL COEFFICIENT 

An experimental coefficient for use in connection with the 
Lorenz formulas has been computed from the data of the Wis 
consin experiments. The method used in making this compu 
tation is explained in detail below. 




O .02 .04 .06 .08 JO J 2 .14 J6 .18 

Discharge of Tree Air in Cubic Feet per Second 

Fig. 19.— Loss Due to Friction in Air Pipe and Air Nozzle. 



Loss Due to Friction in Air Pipe and Nozzle. — A considerable 
loss of energy was caused by the drop in pressure between the 
point in the air main, where the pressure was measured, and a 
point in the foot-piece opposite the air inlet. The amount of 
this drop in pressure was determined by discharging air at 
various rates through the pump, when all w r ater was drained 
out of it. The indications of the gage gave the head required 
to cause the discharge from the air nozzle, and to overcome the 



[477] 



74 



BULLETIN OF THE UNIVERSITY OP WISCONSIN 



frictional resistances in the air pipe with its elbows and other 
fittings, when discharging 1 into the atmosphere. The curves in 
Pig. 19 show this loss of pressure for various discharges for 
three different lengths of air pipe with the Harris foot-piece. 
The lower curve, for series 1, was plotted from the data of 
Table 2 and shows the loss under the conditions of the appara- 
tus shown in Fig. 10. The upper curve, for series 2-13, was 
plotted from the data of Table 3. For some of these runs the 
length of eduction pipe was 19.32 feet, while during the others 
it was 26.71 feet, but the length of air pipe was constant. The 
middle curve, for series 14 and 15, was plotted from the data of 
Table 4. During these runs the length of eduction pipe was 
41.50 feet, but the air pipe AVas shorter than during series 2-13. 
The length of air pipe was not measured, but it may be seen 
from the lower curve that the loss due to the foot-piece was con 
siderable, as in the conditions of the tests represented by this 
curve, there wa,s only one elbow and less than a foot of air pipe 
between the gage and the nozzle. 

To compute the loss of pressure under operating conditions-, 
that is, when discharging against the pressure Pi in the foot 
piece, it was assumed that fluid friction varies very nearly with 
the square of the velocity and directly with the density. If we 
let 

p a = the loss of pressure, in pounds per square inch, when 

discharging into the atmosphere, 
p x = the loss of pressure, in pounds per square inch, when 
discharging against the pressure pi in the foot-piece, 
v a = the velocity of air in the pipe, in feet per second, when 

discharging into the atmosphere, 
v x = the velocity of air in pipe, in feet per second, when dis- 
charging against the pressure p^ 
q a = the volume of free air discharged, in cubic feet per 
second, 

q x = the volume of air at pressure p b in cubic feet per 
second, 

r = the ratio of compression in atmospheres, 
the following proportion may be written 
Pa : v a 2 r a : : p x : V x 2 r x 

[478] 



DAVIS & WEIDXER — THE AIR LIFT PUMP 



75 



Taking' r a as 1, when discharging into the atmosphere, we 
have 

P ^ V x F x = P a q x r x " I " ' 



X 



v q - ! — — r 

a a o " ? 



Hence it was only necessary to divide the loss as taken from 
the curves in Fig. 19 by the ratio of compression, in order to 
find the loss of pressure when discharging against any pres- 
sure pi existing in the foot-piece. 

Loss of Head Due to Entrance. — -The entrance to the tail-piece 
was square edged during the first 318 runs and the loss of head 
due to entrance was, therefore, assumed to have been equal to 
one-half of the velocity head of the entering water. The maxi- 
mum value of the velocity head during this series of runs barely 
amounted to one per cent, of the total head required to discharge 
the water. During the 1909 experiments the tail-piece pro- 
jected into the water and the entrance head has been assumed 
as equal to the velocity head of the entering water for these 
runs. The entrance head is therefore expresssd as 
l v ! 

h e = ~9~ ^ f° r flush entrance, and (25) 



h _ K 

e t; 



for inward projecting pipe (26) 



Loss of Head Due to Velocity of Discharge. — The velocity or 
discharge is much greater than the entrance velocity, due to the 
fact that the combined volumes of the water and air must be 
discharged through the outlet end of the pipe, while only the 
water enters the lower end. The loss clue to the velocity of dis- 
charge is 



q 4- q 

W i 

a / (27) 
p 



in which v b == the outlet velocity, in feet per second. 

q w = the discharge of water, in cubic feet per second. 
q a = the discharge of free air, in cubic feet per second, 
ap ■ — area of cross section of eduction pipe, in square 
feet. 

[479] 



76 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Loss of Head Due to Elbow. — From experiments made in the 
Hydraulic Laboratory of the University of "Wisconsin it was 
determined that the loss of head due to a 2-inch cast iron elbow 
was equal to* 

H = 0.0202 v 2 

or 

and from comparison of these experiments with others on dif- 
ferent sized pipes, it was concluded that the loss of head was 
independent of the size of pipe.t In estimating 1 the loss due 
to the lVj -inch cast iron elbow in the air lift experiments it 
has, therefore, been computed as 1.3 the velocity head of the 
discharge water, or 

. v 2 o 

h Q =1.3_ (28) 
2g 

The loss of head caused by an elbow or bend is largely due to 
the eddies in the straight pipe following the elbow. The elbow 
at the top of the air lift pump used in the "Wisconsin experi- 
ments was followed by only a few inches of straight pipe, so 
the above formula probably somewhat over estimates the elbow 
loss. 

Loss of Head Due to Pipe Friction and Slip. — The loss of 
head in the straight part of the eduction pipe varies consider- 
ably with the amount of air used, due to the difference in the 
amount of slip of the water past the air at different velocities 
of discharge, but it was not possible to estimate the loss due to 
slip separately from the pipe friction. It was observed in the 
glass eduction pipe that in addition to the uniform gradual 
slip of the water past the air bubbles, there were at times sud- 
den disturbances caused by a considerable quantity of water 
slipping down past a relatively large quantity of air. Loss is 
occasioned by the necessity of again lifting the water which has 
slipped down, and also by the internal friction due to the agita- 
tion of the water caused by the slip and by the pipe friction. 

* See discussion on curve resistance in water pipes, by Geo. Jacob 
Davis, Jr. m Trans. Am. Soc. C. E., Vol. LXII, p. 112. (1909). 
f Ibid p. 109, effect of pipe diameter. 



[480] 



DAVIS & WEIDNEK— THE AIR LIFT PUMP 



77 



If h a = the head produced by the air used per pound of water 
pumped, 

h p — the combined loss of head due to pipe friction and slip,. 
v c = the velocity of the water in the well outside the educ- 
tion pipe at the elevation C in Fig. 3 p. 25. 
and using the symbols already established for the the other 
quantities involved, the equation of energy per pound of water 
pumped, between the outlet and a point in the well outside the 
eduction pipe at the elevation C, may be written as follows: 

v 2 p v 2 p 

o- 2 + — + h c + h a = ^ + — + \ + h e + h o +" h p 
w w 

In computing the losses the velocity of approach has been 
neglected and the velocity v c of the water in the well is taken 
as 0. To illustrate the method of computing the friction factor, 
the following data of run No. 338 will be used. 

Length of eduction pipe = 19.32 feet. 

Depth of submergence = 1.312 X 13.6 + 1.104 — 3.00 = 15.95 
feet. 

Diameter of tail-piece = 1% inches, /. area = 0.01227 square 
feet. 

Diameter of eduction pipe = 1% inches, area = 0.00852 
square feet. 

Length of pipe = 19.50 feet, including a short nipple at dis- 
charge end of eduction pipe, .'. — = 187 

Discharge of water = 0.0322 cubic feet per second, or 2.01 
pounds per second. 

Quantity of air used = 0.1111 cubic feet per second = 0.1111 
-~ 13.093 = 0.008481 pounds per second. 

Total discharge, air and water = 0.1433 cubic feet per sec- 
ond. 

Entrance velocity == v t = 0.0322 0.01227 = 2.62 feet per- 
second. 

v 2 

Entrance velocity head= —k = 0.106 feet. 

v 2 

Entrance loss of head = — = 0.106 feet. 

2g 



[481J 



78 



"BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Outlet velocity = v b = .0.1433 -r- 0.00852 = 16.8 feet per sec- 
ond. 

V 2 ( 1 ft Q) 2 

Outlet velocity bead = _J?= „ A '°' = 4.389 feet. 
J 2g 64.32 

Elbow loss of bead = 1.3 X 4.389 = 5.706 feet. 

Barometric pressure = p b = 28.95 X 0.4912 = 14.22 pounds 
per square inch. 

Pressure in air pipe — p g = 1.376 X 5.894 + 28.95 X 0.4912 
= 22.33 pounds per square inch. 

Pressure in foot-piece = Pi = 22.33 pounds per square inch 
minus loss in air pipe and nozzle. Loss when discharging into 
the atmosphere = 1.36 pounds per square inch (from curve Fig. 
19). Loss when discharging against the pressure p 1 = l*36-s i - 
22 33 

- = .897 pounds per square inch. .". pi = 22.33 — .897 = 

21.433 pounds per square inch. 

Energy per pound of air used = 11,350 foot pounds. (Curve 
Fig. 18.) " 

Weight of air used — 0.008481 pounds. 

" Energy of air used per second = 11350 X 0.008481 = 96.26 
foot pounds per second. 

Energy of air per pound of water pumped = h a = 96.26 
2.01 = 47.89 foot pounds. 

Head due to atmospheric pressure = 14.22 X 2.308 = 32.82 
feet. 

P 

The pressure head — : was equal to the submergence plus 

w 

the head due to atmospheric pressure. The datum plane was 
taken at C in Fig. 3 making h c = 0. The values found above 
may be substituted in the energy equation as follows : 
■0 + (15.95 + 32.82) + + 47.89 = 4.389 + 32.82 + 19.32 + 
0.106 + 5.706 + h p . 

\ =34.32 feet, 
h 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



79 



In the manner above described the values of the friction fac- 
tor c p have been computed for most of the runs of series 1 and 
for a few runs in some of the other series. The results are 
given in column 14 of Table 1. These values of the friction 
factor have been plotted as ordinates against the velocities, 
designated as Vi, of the water in a IVi-inch tail piece as ab- 
scissas. The velocities in a tail-piece of the same size as the 
eduction pipe were used instead of the actual velocities in the 
1%-inch tail-piece, so as to make it possible to compare the 
values of c P with the friction factors for unmixed water flow- 
ing in a pipe of the same size as the eduction pipe. In Fig. 20 
the numbers adjacent to the points indicate the ratio of 
volume of free air used to volume of water pumped for each 
run. Curves have been sketched in to indicate the relation be- 
tween c P and Vi for given ratios of air to water. Before the 
regular runs were begun on the air lift, a number of runs were 
made with no air, for the purpose of determining the normal 
pipe friction in the eduction pipe, which, it will be remem- 
bered, Avas largely made of glass. The friction factors com- 
puted from these preliminary runs are also plotted on Fig. 20. 
It may be seen in this figure that these normal friction values 
agree very closely with the values computed from Fanning 's 
table of friction factors for clean iron pipe. It may also be 
seen that when pumping with air the friction factors are very 
much larger than when only Avater is flowing through the pipe, 
but the value of c p does not increase with the ratio of air to 
water but instead it rapidly decreases as the ratio increases 
from small values, apparently reaching a minimum value 
when an excessively large amount of air is used. This may be 
due to the fact that when very small amounts of a;'r are used, 
the air bubbles rise through the water without causing much 
discharge, the energy of the air being mostly used up in 
causing eddies in the water in the pipe. 

The value of the friction factor, computed as described 
above, seems to be entirely independent of the percentage of 
submergence and of the lift. The values, however, decrease 
with the length of pump, which may be seen by reference to 
Fig. 20, the points for the 26.74-foot length falling a small 

[483] 



so 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



distance below the curves, while the points for the 41.50-foot 
length fall a relatively larger distance below the curves. The 
curves shown in Fig. 20 are therefore of no practical impor- 
tance, and it would seem that for a theoretical design of an air 
lift pump, the law of variation of c p with both the diameter and 
length of pump would have to be known. 




.02 



O 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 

Velocity of Water in Toot -Piece 
Pig. 20— Coefficient of Pipe Priction and Slip. 

o = Length of Pump 19.32 Feet 
□ .= " " " 26.74 " 

A = " " 41.50 " 



[484] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



81 



EXPERIMENTAL RELATIONS 

The experiments made by the writers were planned to de- 
termine, first, the effect on the discharge and efficiency of 
variations in the working conditions of the arr lift pump, such 
as variations in submergence, lift and quantity of air used, 
and second, the effect on the discharge and efficiency of 
changes in the structural features of the pump. The first part 
of the following d : scussion relates to experiments in which all 
structural features were the same. 

Relation op Discharge to Ate Used 

The relation between the quantity of air used and the quan- 
tity of water pumped is shown in Fig. 21 for each of the runs 
of the first series. The small figures, by the plotted points, 
indicate the percentage of submergence obtaining during the 
run represented by the point. Curves have been interpolated 
between the points to indicate the discharge of the water for 
varying quantities of air under constant conditions of sub- 
mergence and lift, for each five per cent, submergence from 35 
to 115 per cent. These curves were first sketched in freely, 
interpolating by eye to locate their positions, and were after- 
wards adjusted to harmonize with the curves in Fig. 22. Each 
of these curves was plotted by reading horizontally across 
Fig. 21 the percentage of submergence corresponding to given 
quantities of air for a constant discharge of water. The trial 
curves in Fig. 21 were then shifted slightly until the points 
picked from them fell on smooth curves in Fig. 22. 

Fig. 21 shows that for any given percentage of submergence 
an increase in the amount of free air used, starting with zero 
quantity, causes an increase in the discharge of water up to a 
given quantity of air, beyond which the discharge of water 
decreases with a further increase of air. The quantity of air 
giving a maximum discharge of water is not a constant for the 
different percentages of submergence, nor is the ratio of the 
volumes of air and water constant for the maximum discharge 
6 [485] 



b 




Z6 




.01 .02 .03 .04 .05 .06 .07 .08 .09 .10 .11 .12 ./5 ./4 .15 
Cubic Feet of Air per Second 

Fig. 21.— Relation of Discharge to Air Used.— Series 1. 



[486] 



DAVIS & WBIDNEE — THE AIR LIFT PUMP 



S3 



at different percentages of submergence. The quantity of air 
giving the maximum discharge is less, both absolutely and 
relatively, for high percentages of submergence than it is for 
low percentages of submergence. 

From the curves of Figs. 21 and 22, it appears that for any 
given rate of air consumption, the discharge of water increases 
indefinitely as the percentage of submergence increases In 
this connection these curves are likely to be misleading unless 
the conditions of the experiments are borne in mind. All of 
the experiments represented by the points in Fig. 21 were 
made with a constant length of pump of 19.32 feet. There- 
fore, an increa.se in the submergence was necessarily accom- 
panied by a decrease in the lift, the latter becoming zero at 100 
per cent., and negative at lu'gher percentages of submergence. 
That is, at percentages greater than 100 per cent, there was a 
head on the outlet of the pump which caused a flow without the 
use of any air, as in the case of artesian wells. In commercial 
plants using the air lift system of raising water, the pump is 
of fixed length designed and built to work at some definite 
percentage of submergence. In many cases the water level 
in the well is not correctly estimated for working conditions, 
or the conditions existing at the time of installing the well 
may be changed by the operation of other wells in relatively 
close proximity, so that it is often found that the relation of 
lift to submergence in the case of many pumps is far from 
what it should be. The large variations in the discharge which 
may result from such changes in the percentage of submer- 
gence are clearly indicated in Figs. 21 and 22. 

Eelation of Output to Percentage of Submergence 

As to the question of what is the best percentage of sub- 
mergence to adopt in the design of a pump to lift the water a 
definite height, no information is given in Fig. 21, for the 
reason that it is impossible to determine from this diagram 
whether the increased discharge of water is due to the increase 
in the percentage of submergence or to the accompanying de- 
crease in the lift. 

In order to throw more light on this subject Figs. 23, 24 and 

[487] 



84 BULLETIN OP THE UNIVERSITY OF WISCONSIN 

ainuij^j jad j^io/^ j.o 9uo|jDg 




[488] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



85 



SO 




30 40 50 60 70 80 90 /Q 

Submergence in Percent 

Fig. 23.— Relation of Output to Percentage of Submergence.— Series 1. 



25 have been plotted. The method of constructing these curves 
is as follows: Choosing some definite rate of air consumption, 
as for example 0.03 second feet, and reading vertically along 
this air line in Fig. 21, the discharges were obtained for each 
five per cent, submergence. These quantities were then multi- 
plied by the lift in feet for the corresponding submergences. 
This gave the work output, expressed in foot gallons, for each 
five per cent, submergence. In order to avoid confusion, part 
of the curves, those for the rates of air from 0.03 to 0.07 second 
feet have been plotted in Fig. 23 and the remainder 'n Fig 24. 
The curves are shown only as far as 100 per cent, submergence. 



[489] 



86 



BULLETIN OF THE UNIVERSITY OP WISCONSIN 



80 




50 40 50 60 70 80 90 100 

Submergence in Percent 

Fig. 24.— Relation of Output to Percentage of Submergence.— Series 1. 



Beyond that limit the output is negative on account of the lift 
being negative, and the curve extends in the general direction 
indicated by the part near the 100 per cent, submergence point. 
In-as-much as the discharge increases from zero, while the lift 
decreases from a maximum value to zero as the percentage of 
submergence increases, there is necessarily a maximum point 
on the curve. The maximum points for all the curves lie between 
60 and 65 per cent, submergence. The percentage of submerg- 
ence giving the maximum output is shown for various rates of air 
consumption by the curve in Fig. 25. In this figure is shown 
also the relation between air consumption and maximum output. 



[490] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



87 



By inspection of these two curves it may be seen that the maxi- 
mum output occurred when the rate of air consumption was 
about 0.09 second feet and the percentage of submergence was 
about 61. Since the lift corresponding to 61 per cent, sub- 
mergence was 7.55 feet, the maximum output of 73.2 foot gal- 
lons represented a discharge of 0.0215 second feet of water. 



70 



60 

























































r oo 


t 


3q/ 
























c 
















































































































































































































































— N 






































\l< 


) 


































K c 


a 














































































»c e for 


M 


ax. ( 


Dut 


Dut 


































I 







.03 .06 .09 .12 .15 ~ JQ 



Free Air , Cubic Feet per Second 

Tig. 25— Relation of Quantity of Air Used to Maximum Output and to Percentage of 

Submergence. — Series 1. 

Hence, for maximum output the ratio of volumes of air to 
water was 0.09 -f- 0.0215 — 4.2. The curves are based on ex- 
periments on a single length of pump of 19.32 feet. Some ex- 
periments on pumps of different lengths show that for the 
same air consumption and percentage of submergence the out- 
put increases with the length of pump, therefore the outputs 
in foot gallons shown on Figs. 23, 24 and 25 must be regarded 
as applying only to the 19.32-foot pump. The experiments on 
the longer pumps were taken at only two submergences, of ap- 

[491] 



88 BULLETIN OF THE UNIVERSITY OF 'WISCONSIN 

proximately 40 and 80 per cent., so curves similar to those of 
Figs. 23 and 24 could not be drawn for the longer pumps ; but 
the points for these runs plot in such a way as to indicate that 
the maximum point must be about the same percentage of sub- 
mergence as for the shorter pump. 

The curves of Figs. 23 and 24 seem to be parabolas having 
the equation 

(y — y')=m ( X — x') n (30) 

in which 

y — the output in foot gallons. 

y' = the maximum output in foot gallons. 

x = submergence in per cent. 

x' = submergence in per cent, corresponding to maximum 
output. 

By taking the values of x' and y' for any given value of air 
from Fig. 25, and subtracting them from the values of x and y 
taken from the curves of Fig. 23 for the same value of air, 
the values plotted in Fig. 26 were obtained. The symbols with 
horizontal bars attached represent points of the curve on one side 
of the vertex while the plain symbols represent points on the 
other side of the vertex on the -same curve, The points near the 
lower end of the diagram scatter somewhat. These points cor- 
respond to points very near the vertex of the parabolas and 
the divergence from the mean line simply indicates a very 
small error in the values of x' and y r , which were found by 
trial. The substantial agreement of the points with the line 
shows that for the 19.32-foot pump, the output varies in ac- 
cordance with the parabolic law and that for all rates of air 
consumption the values of m and n are the same. Using the 
values of m and n determined from the mean line of Fig. 26 
the equation of the curves becomes 

y-y'= 0.028 (x-xT* 15 (31 



[492] 



DAVIS & WEIDNER— THE AIU LIFT PUMP 



150 



> 5 



3 



120 

100 
90 
80 
70 
60 
50 

40 














~3> 


























































f 


























































t 


















2 




















f 






































h 
























































30 
20 






f 






















■ 








50 60 7 






I 










\ 


































30 40 










o / 




g=0.03 Second Feet of A 
□ = 0.0 4 « . ' - 
a =0.05 » - - . 
v=0.06 - - - 
0=0.07 « 


































-0- / 













































































e 7 & 9 \0 15 20 

X- X ' 

Fig. 26— Logarithmic Plotting of Output— Percentage of Submergence Curves.— 



[493] 



90 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 









1 


A 


x 


}9 


































• - ! 




\\\ 






































so 


V 






































\ 


\ 




































39o\ 


) \ 


\ 


f 


































38% 


6 A 


\ 




































3 o P 




\ 


v o \a\ 


































} d a 


\\ 












































































> 


V 




f 


































fie 


V 






































o 

55 P 






































fen 




\ 










































































jsa 








W 


If*' 




























3«e< 


\ 






So- 






























SSI, 






SI 






a 
































N 


k£ 


--- 
































A" 






160 










3.6 


























o 



















































































































































































































































































































































25 50 75. ~ 100 



v Input in Foot-Pounds per Second 

Tig. 27.— Relation of Efficiency to Input with Constant Length of Pump. Runs (1-86) 

Series 1. 

Relation of Efficiency to Input and Percentage of Sub- 
mergence with Constant Length of Pump 

If the quantity of free air used were a measure of the work 
input then the curves of Figs. 23, 24 and 25 would show the 
submergence to adopt for maximum efficiency at any given 
rate of air consumption, but such is not the case. An increase 
in the percentage of submergence, in the case of a pump of 
fixed length, results in a greater depth of submergence of the 
air inlet and consequently in an increased air pressure. With 
a constant consumption of free air the work input varies with 
the submergence. In order to show the effect of variations in 
the submergence and input on the efficiency of operation the 
curves in Figs. 27, 28 and 29 have been drawn. 

[494] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



91 




Fig. 28.— Relation of Efficiency to Input with Constant Length of Pump. 
Runs (87-202) Series 1. 



Efficiency and Input. — The efficiencies computed from runs 
(1 — 202) of the first series of experiments have been plotted 
as ordinates against the corresponding inputs in Figs. 27 and 
28. In order to avoid confusion of lines the points with per- 
centages of submergence lower than 63 were plotted in Fig. 27 
and those above were plotted in Fig. 28. These curves show 
that for any given constant percentage of submergence and 
constant length of pump, the efficiency increases very rapidly 
as the input decreases. Efficiencies higher than those shown 
on the diagrams have only slight practical importance on ac- 
count of the small discharge of water obtainable when working 
at such low rates of input, and the consequently high initial 
cost of the well in proportion to the discharge. 



[495] 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Efficiency and Percentage of Submergence. — The curves in 
Figs. 27 and 28 also show that, if the total length of eduction 
pipe remains constant, the maximum efficiency for a given 
input or rate of pumping is obtained at about 63 per cent, sub- 
mergence. This is more clearly shown in Fig. 29, which was 
drawn from values taken from the average curves of Figs. 27 and 
28. It will be seen frcm these diagrams that with a given input, 

34 





































































\ 


v 








































\ 




























J. 














r 


























1 














\ 


































































/ 






n-i 


■bs. 1 












































































6°. 








































■10 




































/ 




ftO 




































/' 




90, 










\ 


























/ 




too 
















1 




























120- 
140- 




























































































1 


n 











































<+■ 16 
'<+- 

14 
12 



10 



30 40 50 60 70 

Percentage o"P Submergence 



80 



90 



100 



Fig. 



29. — Relation of Efficiency to Percentage of Submergence with Constant Length 
of Pump —Series 1. 



the efficiency first increases with the percentage of submerg- 
ence until a maximum is reached at about 63 per cent., and then 
decreases with a further increase in the percentage of sub- 
mergence ; becoming zero at 100 per cent, submergence and 
the efficiencies having negative values when the percentage 
of submergence is greater than 100, because for such cases the 
lift has a negative value. The efficiency curves are not drawn 
for submergences greater than 100 per cent. The total length 

[496] 



DAVIS & WEIDNER— THE AlR LIFT PUMP 



93- 



of eduction pipe, however, remaining constant, the lift varies 
as the percentage of submergence is changed. 

Relation of Efficiency to Input and Percentage of Sub- 
mergence With a Constant Lift 

In comparing the results of the Wisconsin experiments there 
are five variables to be considered; namely, the lift, the sub- 
mergence, the discharge, and the quantity and pressure of the 
air used. In the previous discussion the effect of varying some 




O 20 40 60 80 100 120 140 160 180 200> 

Input in Foot-Pounds per Second 
Fig. 30.— Relation of Efficiency to Input with a Constant Lift— Series 20. 



of these factors has been shown, but on account of the fact that 
the lift varied inversely as the submergence, the methods of 
comparison used on the preceding pages do not give definite 
information as to the best submergence to use with a constant 
lift. The practical problem in most deep well propositions is 
to determine at what percentage of submergence the maximum 
efficiency will be obtained for a given lift. The curves of 

[497] 



94 



BULLETIN OP THE UNIVERSITY OF WISCONSIN 



Figs. 30 and 31, plotted from the data of series 20, show this 
information. In this series the lift was kept constant at five 
feet and the percentage of submergence was varied by chang- 
ing the length of pump. 

Efficiency and Input. — Fig. 30 shows that for any given con- 
stant percentage of submergence and constant lift, the effi- 

36 



32 



28 



24 



o 20 
16 

LA 



12 



























4 






4 










































































t 




4 
L 






































4 






4 






























/ 




4 




L 




/ 


































/ 




/ 




























-i 




i 






/ 






























4 












4 






\ 
\ 




















<> 


• 


z 
















\ 




















/ 








/ 


i 
































T 




































t 




/ 




h 




































■ ,5 


V 












































/ 






































































































i 





































































10 



20 



80 



90 



100 



30 40 SO 60 70 

Percentage o"f Submergence 

Fif. 31.— Relation of Efficiency to Percentage of Submergence with a Constant Lift. — 

Series 20. 



ciency increases as the input decreases, which checks the con- 
clusion drawn from the curves of Figs. 27 and 28. 

Efficiency and Percentage of Submergence. — Fig. 30 also shows 
that with a constant lift, the efficiency increases as the percent- 
age of submergence increases, for all rates of input and all 
practical percentages of submergence. This result is quite 
different from that obtained when the length of pump remained 
constant and lift varied, as may be seen by comparing the 
curves of this figure with those of Figs. 27 and 28. The above 



[498] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



95 



conclusions may perhaps be more plainly seen by reference to 
Fig. 31, which was plotted for the purpose of comparison with 
the curves of Fig. 29. The curves of Fig. 31 show a tendency 
to reverse after passing the ordinate at 90 per cent, submerg- 
ence. This may be understood if one reflects that between 90 
and 100 per cent, the length of pump increases very rapidly 
with any constant lift, reaching infinity at a submergence of 
100 per cent. Hence, the efficiency will decrease very rapidly 
as the percentage of submergence is increased from a point near 
90 per cent, submergence to a submergence of 100 per cent., 
as indicated by the broken curve for an input of 70 foot pounds. 

Relation oe Discharge and Efficiency to Lift 

In discussions of the air lift the statement is frequently made 
that an increase in the lift causes a reduction in the discharge 
and in the efficiency, other conditions remaining constant. That 
this statement is not true in all cases is proved by the curves 
shown in Fig. 32, in which are plotted the results of three series 
st} \ — i — i — i — i — ri — i — i — i — i — i — i — i — i — m — r— i — i — i — m — i — i — r-|— i — n — \*s 



45 




50 100 150 " 200 "' 250 500 



Input in Foot-Pounds per Second 
Fig. 32. — Relation of Discharge and Efficiency to Lift. 

= Series 4— 1%-Inch Harris Foot-Piece— Length of Eduction Pipe 19.32 Feet— Aver- 
age Lift 3.29 Feet— Average Submergence 82.97 Per Cent. 

=: Series 11— 1% -Inch Harris Foot-Piece— Length of Eduction Pipe 26.74 Feet— Aver- 
age Lift 4.74 Feet— Average Submergence 82.40 Per Cent. 

= Series 14— 114-Inch Harris Foot-Piece— Length of Eduction Pipe 41.50 Feet— Aver- 
age Lift 7.66 Feet — Average Submergence 81.54 Per Cent. 

[499] 



96 



BULLETIN OF THE UNIVERSITY OP WISCONSIN 



of experiments made in order to show the effect of varying the 
lift, other conditions remaining the same. The same foot-piece 
and size of eduction pipe were used in all these series, the sub- 
mergence was kept nearly constant, at about 82 per cent., and 
the lift was varied by adding extra pipe to the discharge end 
of the eduction pipe. This diagram shows, that for a given 
input, the discharge and hence the efficiency, increases with 
the lift and the length of eduction pipe ; the percentage of sub- 
mergence and all other conditions, except the length of the 
pipe, remaining constant. 

A similar result was obtained at a smaller percentage of sub- 
mergence, as is shown in Fig. 33. In this diagram the dis- 



































































































































































































-b- 












\ 
















































X 










































\ 










































































6 






v= 
















































n 


b, 


















i 


t 


f 




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' SO 100 150 200 

Input in Foot-Pounds per Second 
Fig. 33.— Relation of Discharge and Efficiency to Lift. 



Feet— Aver- 



= Series 7— 114-Inch Harris Foot-Piece— Length of Eduction Pipe 19.32 
age Lift 10.88 Feet— Average Submergence 43.66 Per Cent. 

R — Series 10— 114-Inch Harris Foot-Piece— Length of Eduction Pipe 26.74 Feet— Aver- 
age Lift 15.73 Feet— Average Submergence 41.19 Per Cent. 

^ = Series 15— 114-Inch Harris Foot-Piece— Length of Eduction Pipe 41.50 Feet— Aver- 
age Lift 23.47 Feet— Average Submergence 43.45 Per Cent. 

$ = Series 6— 114-Inch Harris Foot-Piece— Length of Eduction Pipe 19.32 Feet— Aver- 
age Lift 11.40 Fteet— Average Submergence 40.97 Per Cent. 

charge curve for a lift of 15.73 feet lies below that for a lift 
of 10.88 feet, although for a given input the efficiency is greater 
for the larger lift. This apparent disagreement with the law 
seeming to hold for the other series of runs plotted, was doubt- 

[500] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



97 



less due to the fact that the percentage of submergence was 
different in the two series of runs. It was difficult in setting 
up the apparatus and adjusting the valves to get exactly the 
same percentage of submergence in the different series, or even 
to maintain the percentage constant for all the runs of a series. 
To show the difference in the discharge due to the variation 
in the percentage of submergence the discharges for series 6 
have been plotted in Fig. 33 and a dash line has been drawn 
through them. The average percentage of submergence for 
these runs was 40.97 and the lift 11.40 feet. By comparing this 
curve with that for series 10, which was made with practically 
the same percentage of submergence, it may be seen that the 
discharge with the higher lift of 15.73 feet was considerably 
greater than the discharge with the lift of 11.40 feet. The dis- 
charge curve for the 15.73-foot lift would therefore have plot- 
ted higher, between the curves for the 10.88-foot and the 23.47- 
foot lifts, if the conditions of submergence had been the same 
in the three series of runs. 

The reason for an increase in the discharge occurring when 
the length of pump is increased may be understood by study- 
ing the theoretical relations of the various quantities involved, 
as expressed in equation (17) of the Lorenz theory (see p. 28). 
By transposing this equation and restoring u b which had been 
cancelled out from equation (12) it may be made to read 
/ P P. \ 2g a 2 

1 W = \ tU__S (32) 

2 g h a' 2 _l / 1 i c _i_ ) q _|_ q ) _l c q 2 

To adapt this formula to the conditions of the Wisconsin ex- 
periments, 1.3 must be added to the quantities in the first par- 
enthesis of the denominator to take account of the loss due to 
the elbow at the top of the eduction pipe. With this change, 
equation (32) becomes 

/ P P. \ 2g a 2 

2-303 ^ yHS„f K\V^ 

w 



(33) 



2gh a 2 _L/ 2 .3-h c — V f V4- ^ V + c q 2 
1 p 1 ^ • 1 b d / \ 13 w / e w 

Curves showing the relation of the discharge, q w , to the lift 
7 [5011 



98 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



hi, have been computed by means of this formula for three dif- 
ferent percentages of submergence, and are plotted in Fig. 34. 
The conditions assumed were as follows: 

Area of eduction pipe == 0.00852 square feet. 

Percentages of submergence = 40, 60, and 80 per cent. 

Barometric pressure = 14.3 pounds per square inch. (The 
approximate average pressure during series 1.) 

Input at piezometer on air pipe = 100 foot pounds. 

In the numerator of equation (33) the expression 



represents the input at the air inlet in the foot-piece. In the 
1909 experiments the pressure, from which the input w T as com- 
puted, was measured at a point on the air pipe some distance 
from the foot-piece. The pressure, so measured, therefore, in- 
cludes the loss in a section of air pipe of length sufficient to 
reach from the top of the w r ell to the foot-piece. This loss 
should be charged to the pump, for such a length of air pipe is 
inevitable. Hence, in computing the quantity of air used at 
any given rate of pumping and at any lift, the gage pressure, 
p g , should be used instead of the pressure, p i? in the foot-piece. 

/ P b P o-\ 

Putting qbUb 2 . 303 — loff 10 — - = 100, the assumed input, 

\ b P b' 

the quantity of air used per second was computed for the gage 
pressures corresponding to the various lifts and percentages 
of submergence. The gage pressure, p g , was computed, for the 
assumed conditions, by adding 14.3 pounds per square inch, 
to 0.434 times the depth of submergence in feet, plus the loss of 
head due to friction in the air pipe and nozzle, minus the loss 
due to entrance and velocity in the foot-piece. Since the loss 
of head due to friction in the air-pipe and nozzle is a function 
of the volume of air used, it was necessary to first assume the 
volume of air in order to estimate the approximate loss of head 
due to air friction from the curve of Fig. 19 as explained on 
page 75. By making a few approximations in this way, the 
proper value of p g and the corresponding value of q b were 
found. An assumed value of the discharge q w was used to com- 




[502] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



99 



pute the ratio of volume of free air to volume of water and the 
ratio of discharge to area of eduction pipe which were used as 
arguments in estimating the friction factor c p from Fig. 20. 
By making a few such approximations, corresponding values 
of c P) q a , and q w were found which satisfied equation (33). 

With constant percentage of submergence, an increase in the 
lift causes a proportionate increase in the depth of submergence 
and, therefore, a proportionate increase in the pressure. As 
the air pressure increases with the lift, the quantity of ^ree 
air per given input will decrease as the lift increases. The 

































































































































































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.004 .008 .012 .0/6 .020 .024 .028 

Discharge of Water in Cubic Feet per Second 
Fig. 34.— Relation of Discharge to Lift with Constant Input. 



numerator of equation (33), therefore, increases slightly as 
the lift increases, because the loss in the air pipe is less with the 
smaller volume of air and consequent lower velocity. Also, 
since q w is small compared with q b , an increase in the lift de- 
creases the value of the second parenthesis in the denominator 
of equation (33). c p varies with the velocity of the water in 
the foot-piece and with the ratio of volume of free air to vol- 
ume of water. It was found, in computing, that the relation 
of these quantities was such as to make c p increase with the lift 
and that the last term in the denominator, which is a function 
of the entrance loss, was practically negligible. The middle 
term of the denominator proved to be the controlling one in 
the determination of the shape of the discharge-lift curve. 



[503] 



100 BULLETIN OP THE UNIVERSITY OF WISCONSIN 

With the first parenthesis increasing in value and the second 
decreasing with the lift, evidently their product must have a 
maximum value at some point. The points of maximum dis- 
charge, as shown by the curves of Fig. 34, do not agree with 
the indications of Figs. 32 and 33, which show the discharge 
increasing up to higher lifts. This discrepancy is explained by 
the fact that for a given velocity of water in the foot-piece and 
given ratio of volumes of air to water the friction factor c p de- 
creases with the length of pump, as pointed out on page 79. 
In-as-much as the law of this variation is not known, the value 
of c p was necessarily assumed independent of the lift, and in 
making the computations the values were taken from the curves 
of Fig. 20. It may be seen, however, by reference to equation 
(33), that if c p decreases with the lift, other things being con- 
stant, the maximum discharge would have occurred at a higher 
lift under the assumed conditions and the curves of Fig. 34 
would have tended to check the experimental results. 

Effect of Compressed Air Outside of Pump 

"When the Harris foot-piece was purchased the manufacturers 
furnished it with fittings for introducing compressed air into 
the well casing outside of the pump, but the apparatus as used 
in the 1908 experiments did not permit any runs under these 
conditions. The statement is made in the Harris patent (No. 
758360) that "the chief feature consists in combining the idea 
of introducing compressed air or gas into the casing to act upon 
the surface of the water or other fluid to force the same down- 
ward and the use of a suction means, such as an ejector or 
similar means, for drawing up the fluid and expelling it." 
Through correspondence we were informed by the manufac- 
turers of the Harris pump that "the object in the use of this 
outside pressure is to steady the flow of water and retard the 
usual surging up and down occasioned when air is liberated 
in the well. The idea is not to put on excessive pressure, and 
as to the amount of pressure to be used, it depends entirely 
upon conditions and necessarily has to be adjusted on the 
ground to meet the conditions encountered." They further 
stated in this connection that "we find in many cases that by 

[504] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



101 



simply filing a leakage screw allowing a small volume of air 
to leak into the casing that it affords sufficient amount to work 
in harmony with the air pressure leading directly to the pump, 
while in other cases we find that it is often necessary to carry 
25 or 30 pounds on the outside in order to assist in forcing the 
water through the discharge pipe." 

In view of the foregoing it was deemed desirable to make 



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50 100 150 200 

Input in Foot-Pounds per Second 
Fig. 35.— Curves Showing the Effect of Compressed Air Outside of Pump. 

!= Series 3— li/i-Inch Harris Foot-Piece — Length of Eduction Pipe 19.32 Feet — Aver- 
age Lift 3.44 Peet — Average Submergence 82.19 Per Cent. — Compressed Air in 
Casing Connected with Air Main. 

p= Series 4 — l^-Inch Harris Foot-Piece — Length of Eduction Pipe 19.32 Feet — Aver- 
age Lift 3.29 Feet — Average Submergence 82.97 Per Cent. — Compressed Air in 
Casing Shut Off from Air Main. 

= Series 5— l^-Inch Harris Foot-Piece— Length of Eduction Pipe 19.32 Feet— Aver- 
age Lift 3.02 Feet— Average Submergence 84.37 Per Cent.— Annular Air Tube 
System. 



some experiments with compressed air outside of the pump, 
and the apparatus as set up for the 1909 experiments was 
arranged with this object in view. Series 3, 4, 6, 7, 8, 9 and 
10 were made for this purpose. The results are plotted in 
Figs. 35, 36 and 37, which show the efficiency and discharge 
curves for different rates of energy input under different con- 
ditions as to air outside of the pump. In series 3 the air was 
introduced above the surface of the water in the well and was 



[505] 



102 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

in connection with the air main throughout the run, the valve 
in the casing air pipe (see Fig. 15) being open, so that the air 
pressure in the casing remained constant, and in case of any 
leakage from the casing or connections the amount lost was 
included in the amount of air recorded as supplied to the pump. 
In series 4 the air was admitted through the casing air pipe to 
the surface of the water in the well before the run started, and 
after the proper submergence was obtained and the pump was 
working steadily the air in the casing was shut off from the 
main by closing the valve in the casing air-pipe. In case of 
any air-leakage under these conditions the water rose in the 
well, thereby keeping the submergence fairly constant during 
the run. By means of a glass gage connecting with the well 
near the top and bottom, marked well gage in Fig. 15, the ele- 
vation of the water in the well could be noted. During series 
3 and 4 the water level in the well stood at times at various 
elevations lower than the air inlet, but during none of the runs 
did the water surface fall low enough to allow air to enter the 
bottom of the tail-piece. The submergence in both cases re- 
mained practically constant and there was no appreciable leak- 
age from the casing. The points belonging to the two series 
of runs lie on the same curve in Fig. 35, indicating that there 
was no difference in the discharge under the two conditions, 
as was to be expected. 

In the same figure the efficiency and discharge curves are 
plotted for series 5. In this series the same apparatus w T as 
used but the supply to the Harris foot-piece was shut off, the 
foot-piece, however, remaining in the well and the well pumped 
according to the annular air tube system described on page 34, 
all the air used entering through the casing air pipe. As may 
be seen from the diagram the efficiency for this method of 
pumping is very low, but this series of runs, however, should 
not be taken as a criterion for the efficiency of the annular 
tube system, as the apparatus was not properly designed for 
this system of pumping. Obviously the annular space between 
the 1%-inch discharge pipe and the six inch casing was too 
large for efficient pumping. 

Fig. 36 shows the results of series 6 and 7. In both series 



[506] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



103 



the length of eduction pipe was 19.32 feet and the 1%-inch 
Harris foot-piece was used. In series 6 the casing was open to 
the atmosphere so that the submergence was due entirely to 
the water in the well, while in series 7 compressed air was 
introduced above the surface of the water in the well and was 
shut off from the air main. It will be noticed, however, that 
the average submergence differed by 2.69 per cent., which un- 



35 

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200 



Fig. 



O 50 100 150 

Input in Foot- Pounds per Second 
-Curves Showing the Effect of Compressed Air Outside of Pump. 



= Series 6— l^-Inch Harris Foot-Piece— Length of Eduction Pipe 19.32 Feet— Aver- 
age Lift 11.40 Feet— Average Submergence 40.97 Per Cent.— Casing Open to 
Atmosphere. 

= Series 7— l^-Inch Harris Foot-Piece— Length of Eduction Pipe 19.32 Feet— Aver- 
age Lift 10.88 Feet— Average Submergence 43.66 Per Cent— Compressed Air 
in Casing Shut Off from Air Main. 

— Series 1— 114-Inch Harris Foot-Piece— Length of Eduction Pipe 19.32 Feet— Aver- 
age Lift 10.88 Feet— Average Submergence 43.66 Per Cent.— Submergence Ob- 
tained by Means of Overflow Host Shown ifi Fig. 3. 



doubtedly accounts for the higher efficiency for the higher per- 
centage of submergence. In order to show what difference the 
percentage of submergence makes, the points plotted as tri- 
angles were interpolated from the curves shown in Fig. 27 for 
a submergence of 43.66 per cent. The curves in Fig. 27 were 
plotted from the first series of experiments in which the length 
of eduction pipe and foot-piece were the same as used in the 
series under discussion, but the submergence was obtained by 



[507] 



104 



BULLETIN OP THE UNIVERSITY OF WISCONSIN 



means of the overflow hose shown in Fig. 10 corresponding very 
closer/ to the conditions of series 6. As will be noticed from 
the diagram, the points fall very closely on the curve so that 
the conclusion may be drawn that had the percentage of sub- 
mergence remained constant no difference would have been 
noticed in the efficiencies of the two series of runs. With the 



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Fig. 



50 /00 150 200 

Input in root-Pounds per Second 
37.— Curves Showing the Effect of Compressed Air Outside of Pump. 



Series 8— 114-Inch Harris Foot-Piece— Length of Eduction Pipe 26.74 Feet— Aver- 
• age Lift 15.70 Feet— Average Submergence 41.29 Per Cent.— Casing Open to 
Atmosphere. 

Series 9— 1%-Inch Harris Foot-Piece— Length of Eduction Pipe 26.74 Feet— Aver- 
age Lift 16.02 Feet— Average Submergence 40.08 Per Cent.— Compressed Air 
in Casing Connected to Air Main. 

Series 10— 114-Inch Harris Foot-Piece— Length of Eduction Pipe 26.74 Feet— Aver- 
age Lift 15.73 Feet— Average Submergence 41.19 Per Cent.— Compressed Air 
in Casing Shut Off' from Air Main. 



same size and length of pump and the same percentage of sub- 
mergence, the discharge per given input would necessarily be 
equal for the two series, if the efficiencies were equal. 

This conclusion is further justified by a study of Fig. 37. 
In this figure the results of three series of runs have been plot- 
ted, which differ only in the method of obtaining the submer- 
gence, the length of eduction pipe being 26.74 feet and the same 
size and style of foot-piece being used for the three series. The 
submergences remained more nearly constant in this case than 
in the preceding one, and the points are seen to lie very nearly 
on the same curve. In view of the results of these series of 

[508] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 105 

experiments the conclusion seems justified that, other condi- 
tions remaining constant, there is no advantage to be gained 
by introducing compressed air above the surface of the water in 
the well. 

Effect of Type of Foot-Pjece 

Figs. 38 and 39 were plotted from results of comparative 
tests on three different types of foot-pieces. The three differ- 
ent types used were the Harris, the Indiana, and a Tee pump 
which are shown in section in Figs. 11 and 12, and are de- 
scribed on page 57. The conditions during the different tests 
were kept as constant as possible, although, as previously 
stated, it was difficult to maintain the percentage of submer- 
gence the same for the different series. Fig. 38 shows the re- 
sults of three series at a submergence of about 42.5 per cent. 
The highest efficiency for a given input is obtained either by the 
Tee or Indiana pump. The points for the Indiana series do 
not lie on a smooth curve, so no curve was drawn for this series, 
but they will average pretty close to the line drawn for the 
Tee pump. The percentages of submergence for the Indiana 
and Tee pumps were practically the same, while the percentage 
for the Harris pump was about 1 per cent, higher. This higher 
percentage of submergence was, however, in favor of the Harris 
pump, which may be seen by reference to Fig. 27. 

In Fig. 39 are shown the results of three series of runs with 
the same foot-pieces, but at a higher percentage of submergence 
than shown in the preceding figure. It will be seen from this 
figure that the highest efficiency for a given input is obtained 
by the Indiana pump. The percentages of submergence for the 
Harris and Indiana pumps are nearly the same with the differ- 
ence in favor of the Harris pump. The percentage of submer- 
gence for the Tee pump is, however, 2.2 per cent higher than 
the Indiana pump. Correcting for this difference would make 
the efficiency curve of the Tee pump coincide very nearly with 
that of the Indiana pump. The conclusion to be drawn from 
the curves shown in Figs. 38 and 39 is that both the Indiana 
and Tee pumps showed a slight advantage over the Harris 
pump, while the Indiana and Tee pump showed practically the 

[509] 



106 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



same efficiency, as nearly as could be seen from the curves. It 
should, however, be said in favor of the Harris pump that the 
Indiana pump was a l^-inch foot-piece which was reduced to 
1 ^4-inch at the entrance to the eduction pipe. 

The opinion of the writers on this point is that the type of 
foot-piece has very little effect on the efficiency of the pump, 
so long as the air is introduced in an efficient manner and the 
full cross-sectional area of the eduction pipe is realized for 
the passage of the water. Anything in the shape of a nozzle 
to increase the kinetic energy of the air is detrimental. 



50 



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10 



6 i 
5 & 



50 100 150 200 

Input in Foot -Pounds per Second 

-Curves Showing the Effect of the Type of Foot-Piece. 



= Series 15— 1%-Inch Harris Foot-Piece— Length of Eduction Pipe 41.50 Feet— Aver- 
age Lift 23.47 Feet — Average Submergence 43.45 Per Cent. 

= Series 16— l^-Inch Indiana Foot-Piece— Length of Eduction Pipe 42.08 Feet- 
Average Lift 24.20 Feet— Average Submergence 42.50 Per Cent. 

= Series 19— Tee Pump— Length of Eduction Pipe 41.60 Feet— Average Lift 23.96 
Feet— Average Submergence 42.40 Per Cent. 



[510] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



107 



Effect of Diverging Outlet 



Fig. 40 shows the effect of increasing the diameter of the 
ednction pipe at its upper end, thus decreasing the velocity of 
discharge and conserving part of the kinetic energy of the 
velocity head. The two series of experiments were performed 
under similar conditions, with the exception that 7.5 feet of 
2-inch pipe and a 2-inch elbow replaced 7.5 feet of l^-inch 



























































































































































































































































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24 

<?2 O; 

21 | 
Z 



/5 



Fig. 



/0O /50 200 250 

Input in Foot- Pounds per Second 
-Curves Showing the Effect of Type of Foot-Piece. 



z=. Series 14— 1%-Inch Harris Foot-Piece— Length of Eduction Pipe 41.50 Feet— Aver- 
age Lift 7.66 Feet — Average Submergence 81.54 Per Cent. 

= Series 17— 1*4 -Inch Indiana Foot-Piece— Length of Eduction Pipe 42.08 Feet- 
Average Lift 7.63 Feet— Average Submergence 81.95 Per Cent. 

— Series 18— Tee Pump— Length of Eduction Pipe 41.60 Feet— Average Lift 6.5& 
Feet— Average Submergence 84.18 Per Cent. 



pipe and a l^-inch elbow at the upper end of the eduction 
pipe. The enlargement from the 1%-inch pipe to the 2-inch 
pipe was made by means of a standard cast-iron reducer. The 
enlargement of the upper part of the pipe caused a large in- 
crease in the discharge and hence in the efficiency. This dia- 
gram illustrates forcibly the necessity of keeping the velocity 
at the outlet as small as possible. Had the experiment been 
made with a more gradual enlargement, increasing the diam- 

[511] 



108 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



eter at the outlet to a larger diameter, still better results would 
doubtless have beeu secured. 



C 25 

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50 100 150 200 

Input in Foot-Pounds per Second 

-Curves Showing the Effect of a Diverging Outlet. 



<•> = Series 11— 1% -Inch Harris Foot- Piece— Length of Eduction Pipe 26.74 Feet— Aver- 
age Lift 4.74 Feet— Average Submergence 82.40 Per Cent. 

□ — Series 13— l^-Inch Harris Foot-Piece— Length of Eduction Pipe 26.74 Feet— Aver- 
age Lift 4.79 Feet— Average Submergence 82.23 Per Cent.— 7.5 Feet of VA- 
Inch Pipe at Upper End of Eduction Pipe Replaced by 2-Inch Pipe. 



This method of piping the well may be used to advantage 
when the lower part of the well is of a smaller bore than the 
upper part. 



[512] 



DAVIS & WEID"NER — THE AIR LIFT PUMP 



109 



STUDY OF THE SIZE OF AIR BUBBLES 

Reference lias been made, on a previous page, to the fact 
that there is a difference of opinion as to the desirability of 
having the air in small bubbles in the rising column of water. 

Experiments made with small glass tubes generally show 
the bubbles to be of a practically uniform size and of the form 
shown in Fig. 3 (b) ; the horizontal cross-sectional area of the 
bubble being about one-half the area of the pipe bore. Under 
these conditions the bubbles rise with a uniform motion and 
with very little disturbance of the intermediate layers of water. 
The action in a large pipe under operating conditions of veloc- 
ity, etc., are, however, quite different. 

The sixteen feet of glass pipe forming part of the eduction 
pipe used in the "Wisconsin experiments afforded a good oppor- 
tunity to study the action of the air in a pump of commercial 
size, under the conditions of the first experiments. The Harris 
foot-piece used in this series of experiments was designed, as 
shown in Figs. 11 and 12, to discharge the air, in the form of 
a thin shell, through an annular slit in the upper end of the 
nozzle just below the entrance to a contracted tube or sleeve ; 
the evident purpose of the design being to promote such an 
intimate mixture of the air and water as would result in the 
production of small bubbles. If such action occurred, its effect 
was largely lost before the mixture of air and water rose to 
the beginning of the glass pipe, which was about a foot above 
the air nozzle. 

When the air was admitted to the pump at a very low rate, 
so that it simply rose through the water without pumping, the 
bubbles took the form of a single convex lens, with the convex 
side upward. The under side of the bubbles was a practically 
level water surface, and the edges of the bubbles were quite 
sharp. The diameter of the bubble appeared, through the cy- 
lindrical glass walls, to be nearly as great as the diameter of 
the pipe bore. Such bubbles rose through the water with very 
steady uniform motion. Between such bubbles were occasional 

[513] 



110 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

smaller ones, in which the surface tension was great enough to 
cause them to tend toward an oblate spheroid in form, though 
their motion was so irregular as to cause them to go through 
violent contortions. 

As the rate of air admission was increased the longitudinal 
axis of the bubbles was lengthened; the shape of the bubbles 
becoming ovoid, with the bottom still flat, but the edges no 
longer sharp. "With a further increase in the rate of air ad- 
mission this general form of bubble persisted until the vertical 
axis became five or six diameters long. A greater rate of air 
admission caused a discharge of water which altered the con- 
ditions as to actual velocities, pipe friction, etc. 

Under the conditions of pumping it was difficult to observe 
the form of the bubbles precisely on account of the velocity 
with which they shot through the pipe. Under practically all 
rates of pumping the bubbles appeared to be quite uniform in 
length near the foot-piece, being about a foot, or about ten 
diameters, long. The low r er end of the bubble was quite flat, 
but the upper end appeared to have lost the regularity of form 
which was so noticeable at slow rates of air admission. The 
bubbles, in short, appeared as cylindrical pistons of air prac- 
tically filling the pipe. Between the large air bubbles were 
pistons of water, of length about equal to that of the air pis- 
tons. In the lower part of these pistons of water were numer- 
ous small bubbles of air about the size of peas. The upper 
part of the water piston, which consisted principally of water 
which had slipped down past the next large air piston above, 
was clear and free from bubbles. 

As the pistons approached the upper end of the glass pipe 
there were frequent sudden disturbances caused by one of the 
water pistons losing its equilibrium and slipping bodily down 
past the air piston below it, thus making two adjacent water 
and air pistons of double the average length. 

Large bubbles, having greater buoyancy per unit area of 
surface, rise more rapidly through a liquid than do small bub- 
bles. The large bubbles, therefore, overtake the smaller ones 
and coalesce with them. Likewise eddies in the water cause 
bubbles to impinge upon one another and coalesce. It appears 
from the Wisconsin experiments, with the Harris foot-piece, 

[514] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 111 

that the conditions of air admission and flow in the foot-piece 
were snch as to cause most of the bubbles to coalesce within a 
space of a few pipe diameters above the foot-piece. The con- 
ditions of the experiments with the Indiana and Tee foot-pieces 
did not admit of inspection of the air in rising through the 
eduction pipe. 

Experiments made by Professor E. Josse, in which he used a 
section of glass pipe in air lift pumps of 79 and 78 mm. diam- 
eter respectively, showed the action of the air and water to be 
exactly similar to that occurring in the somewhat smaller 
pump used in the present experiments, with the exception that 
his description* would indicate that there are many more 
small bubbles in the water pistons which are described as being 
foam-like. In his experiments the foot-piece was quite similar 
to our Tee foot-piece, but the air was admitted to the eduction 
pipe through a narrow annular slit around the pipe wall. 



* Prof. E. Josse, Druckluft-Wasserheber, Zeit. des Ver. Deutscher In- 
genieure, Band 42, seite 981, Sept. 3, 1898. 



[515] 



112 



BULLETIN OP THE UNIVERSITY OF WISCONSIN 



RESULTS OF PREVIOUS EXPERIMENTS 

While there have been many tests made on actual wells, the 
facilities for varying the conditions of operation or for mak- 
ing accurate measurements of the quantities have been limited, 
and knowledge of comparative tests is, therefore, confined 
chiefly to laboratory tests. Brief outlines of those tests with 
which the writers have become familiar will be found in the 
succeeding paragraphs. 

Browne and Behr Experiments. — The experiments were per- 
formed on a 10-inch well with a depth of 55 feet. The diameter 
of the eduction pipe used was three inches, with lengths of 
51.6, 88.3, and 128.2 feet. The diameter of the air pipe was 1 
inch, and a Pohle foot-piece with a nozzle % inches in diam- 
eter was used. The water was measured by means of a weir 
and the air by volumetric measurement, checked by the flow 
through an orifice. The efficiency, based on the least work the- 
oretically required to compress the air, so that it did not in- 
clude the compressor, ranged from 2 to 53 per cent. The con- 
clusions derived from these experiments were : 

(1) Efficiency for a given lift and submergence was great- 
est when the pressure in the receiver did not greatly exceed the 
head due to submergence. 

(2) Efficiency increased with the percentage of submergence. 

Josse's Experiments. — Experiments performed at the techni- 
cal institute at Charlottenburg, Germany. The comparative 
tests undertaken were: (1) with a lift having a discharge 
pipe 119.75 feet long and corrugations of 2.76 and 3.07 inches 
in minimum and maximum diameter, (2) with a lift having a 
smooth discharge pipe of the same length and 2.76 inches in 
diameter, and (3) with a lift having a smooth discharge pipe 
of the same length and 3.07 inches in diameter. Three com- 
parative tests were made under above conditions, differing in 
the percentage of submergence. The water w T as measured by 
volumetric measurement and the amount of air computed from 
the number of strokes of the air piston and cards taken from 
the air cylinder, which gave the volumetric efficiency 

[516] 



DAVIS & WEIDIS Erv — THE AIR LIFT PUMP 



113 



Computations checked by volumetric measurement and found 
to be sufficiently accurate. The efficiency was calculated from 
the indicated work done in the air cylinder and the lift and 
volume of water raised. 

Conclusions : Under similar conditions the smooth pipe gave 
an efficiency of about 45 per cent., the corrugated pipe about 
25.7 per cent, and about half as much water delivered in the 
case of the corrugated pipe. However, the foot-pieces used 
with the two types of discharge pipe differed, the smooth pipe 
having a foot-piece which discharged the air all around the 
circumference of the pipe, while in the case of the corrugated 
pipe the air was introduced by a simple U bend at the bottom 
of the air pipe, with its free end in the center of the discharge 
pipe. In order to test the influence of this foot-piece, a series 
of experiments were made using the U bend foot-piece with 
the smooth discharge pipe. It was found that at high rates of 
pumping there was practically no difference in the discharge,, 
but that at normal rates the foot-piece discharging the air 
around the circumference of the pipe discharged about 25 per 
cent, more water. 

A series of runs in which the submergence, lift, type of foot- 
piece and size of discharge pipe remained constant, showed that 
by increasing the amount of air the water discharged increased 
to a certain point and then decreased. 

A series of experiments were also made on actual wells from 
which Professor Josse deduced the following conclusions: 
(1) If submergence and lift be kept constant, the amount of 
air per volume of water will not vary much with the size of 
the pump. (2) With increasing lift the volume of air per 
volume of water increases, and hence the efficiency decreases. 
(3) Other things being equal, an increase in the area of the 
discharge pipe of 20 per cent, only increased the discharge 1.2 
per cent. 

The efficiencies varied from 20 to 45 per cent, in the labora- 
tory tests, and from 22 to 28 per cent, in operating wells. 

Kelly's Experiments. — Experiments performed at Preesall, 
Lancashire, on actual wells. Water measured by volumetric 
measurement. Air measured by piston displacement and in- 
dicator cards were taken from steam and air cylinders. Effi- 
8 [517] 



114 BULLETIN OP THE UNIVERSITY OF WISCONSIN 

ciencies were calculated from the ratio of the work done in 
raising the water to the work indicated in the air cylinders of 
the compressor. 

Same general result obtained in regard to efficiency, dis- 
charge and ratio of volume of air to volume of water, when 
one well was working alone or when two or three were work- 
ing together. One well was piped according to the side inlet 
system and three wells were piped according to the annular 
tube system, the air entering the eduction pipes through their 
open ends. The size of air and eduction pipe varied for the 
different wells. In the well piped according to the side inlet 
system, the upper end of eduction pipe was enlarged from 4 
to 6 inches in diameter in order to reduce the velocity of dis- 
charge. Total length of eduction pipe varied from 433 feet to 
323 feet for the different wells. The highest efficiency was 
about 40 per cent., obtained when three wells were working 
together. 

Conclusions : 

(1) Highest efficiency obtained at lowest rate of working. 

(2) Discharge increases as the rate of working increases, 
with a tendency to decrease after the rate of working reaches 
a certain point. 

(3) A percentage of submergence of 60 gave a better effi- 
ciency than one of 50, other conditions remaining the same. 

(4) A well piped with 5-inch eduction and 7-inch air pipe 
gave higher efficiencies than one piped with a 4-inch eduction 
and 6-inch air pipe, other conditions remaining the same. 

(5) The well piped with the side inlet system and diverging 
outlet appeared to give better results than the other wells, 
the cross sectional area of the eduction pipe remaining equal. 

(6) The action of the compressed air in an air lift may be 
either similar to that of a piston in a cylinder, it may form an 
emulsion with the water, or it may produce a combination of 
both, the result depending on the rate of working. The piston 
like layers were obtained with the higher rates of working. 

Darapshy and Schubert Analysis of Experiments- -An analy- 
sis of Prof. Josse's and other experiments, performed by the 
firm of Desenisz and Jacobi, from which the authors deduce an 
empirical formula for computing the amount of air required 

[518] 



DAYIS & WEIDNER— THE AIR LIFT PUMP 115 

per volume of water pumped, and from which by the aid of a 
theoretical analysis, they deduce the following conclusions : 

(1) The lift and velocity remaining constant the efficiency 
increases as the percentage of submergence increases. 

(2) The lift and percentage of submergence remaining con- 
stant the efficiency decreases as the velocity increases. 

(3) The submergence and velocity remaining constant the 
efficiency decreases as the lift increases. 

(4) The percentage of submergence and velocity remaining 
constant the efficiency decreases slightly with the lift. 

A few experiments with glass tubes showed that by adding 
a very short length of pipe to the pump as a tail-piece, the dis- 
charge as compared with the discharge without a tail-piece, 
was first diminished, then increased and again diminished as 
the length of the tail-piece was increased, the supply of air to 
the pump remaining constant. In the case of a 1.88-inch pipe 
the maximum discharge was obtained when the length of the 
tail-piece was about twelve times the diameter. 

Westinghouse Air Brake Go's. Experiments. — An extensive 
series of tests comprising nearly 1,800 different experiments, 
covering nearly 400 different combinations of discharge pipe, 
diameter, lift and submergence, were made by the Westing- 
house Air Brake Co. The results and conclusions of the 
tests have been published, but no numerical data or curves 
showing the relation of discharge, air consumption, etc., have 
been given to the public. The experiments were all made on an 
actual well, 6 inches in diameter and 174 feet deep. The dis- 
charge was weighed and amount of air computed by observing 
the initial and final pressures in a tank of known volume. 
The following conclusions, taken from an article in the Engi- 
neering News of June 18, 1908, indicate what these tests 
showed. 

(1) The rate of delivery of water, and the air consumption 
per gallon, with fixed size of discharge pipe, are practically 
constant for all lifts, provided the ratio of lift to submergence 
is maintained constant. 

(2) "With a discharge pipe of given diameter, the delivery 
decreases and the air consumption per gallon increases as the 
ratio of lift to submergence increases. 

[519] 



116 BULLETIN OF THE UNIVERSITY' OP WISCONSIN 

(3) "With a fixed ratio of lift to submergence, the air con* 
sumption per gallon decreases as the size of the discharge pipe 
increases. 

(4) The least air pressure that will give continuous flow is 
the proper pressure to use. A slightly lower pressure gives 
intermittent delivery, and the amount delivered is much de- 
creased, though the air consumption per gallon is slightly 
lower than with continuous flow. "With pressure higher than 
just enough to give continuous flow, the delivery is increased 
somewhat, but the air consumption per gallon delivered is in- 
creased in greater ratio; and with further increase in air pres- 
sure a point of maximum delivery is reached, beyond which the 
delivery is decreased in amount. The sound of the discharge 
is a reliable guide to proper regulation of the air supply. 

(5) It appears from (2) that by increasing the submergence, 
i. e. locating the foot-piece deeper down in the water, for a 
given lift, the air consumption is progressively reduced. But 
as the required air pressure is increased with the greater depth, 
a cubic foot of air represents greater power. A curve repre- 
senting the variation of horsepower required per gallon of 
water delivered, with depth varying, shows that the power 
first decreases with increasing depth, then reaches a maximum 
and thence increases. The ratio of lift to submergence at this 
minimum point may be called the "economical ratio." 

(6) For a given size of discharge pipe the economical ratio 
decreases as the lift increases ; i. e. the submergence should be 
increased in greater ratio than the lift. For a given lift, the 
economical ratio increases (submergence decreases) as the size 
of discharge pipe increases. 

(7) A tail-piece or projection of the discharge pipe below 
the air inlet is essential in starting, as it tends to prevent 
the air from backing down into the well and rising in the cas- 
ing outside the discharge pipe. 

(8) Anything in the shape of a jet or pipe introduced into 
the discharge pipe to serve as an air inlet has no value, and is, 
in fact, detrimental by forming an obstacle to the free pas- 
sage of water. 

(9) The size of the air pipe is determined only by consid- 



[520] 



DAVIS & WEIDNj^R — THE AIR LIFT PUMP 



117 



erations of friction loss required to force the air through the 
pipe. 

Duty Tests 

The published results of duty tests on air lift plants are 
few in number. The plant is usually so arranged that a duty 
test is rather difficult to make, as the compressor takes steam 
from the same main as the force pumps. In order to give the 
reader an idea of the performance of an air lift plant figured 
on a duty basis, the following published tests are herewith 
appended : 

"The plant at Atlantic City, N. J., showed a satisfactory 
duty ranging roughly from 20,000,000 to 25,000,000 foot 
pounds work per 1,000 pounds of dry steam. The pumping 
plant comprised a Rand duplex flywheel compressor, having 
10-inch and 16-inch cross compound steam cylinders of 12-inch 
stroke, 13xl2-inch air cylinder, Corliss inlet valves, and poppet 
discharge valves; a compressor of the same type with 11-inch 
and 18xl4-inch stroke steam end and 16xl4-inch air end, hav- 
ing Meyer adjustable valves on the steam cylinders; a Wain- 
wright surface condenser; a Deane combined wet vacuum and 
circulating pump, with 5V2 x 7-i n ch steam end and 6x7-inch 
pumps; an air receiver 28 inches by 8 feet; and galvanized 
piping to the wells, with valves. The smaller compressor was 
to be in reserve. The contract price for the pumping equip- 
ment complete was $8,250. Plant consisted of 13 wells with 
a capacity of about 5,450,000 gallons per 24 hours. The aver- 
age lift is about 27 feet and submergence about 60 per cent." 

"A comparison between the efficiency of wells pumped with 
air lift and steam deep well pumps at Waukesha, Wis., showed 
an efficiency of between 16 and 18 per cent, for air lift based 
on I. H. P. in steam cylinder and an efficiency of 74.8 per cent, 
for deep well pumps based on I. H. P. of engine." 
Air Lift. 

Duty per 100 pounds of coal 8,200,000 foot pounds 

Duty per 1,000 pounds of steam. . .11,940,000 foot pounds 
Deep Well Pumps. 

Duty per 100 pounds of coal. .... .34,500,000 foot pounds 

Duty per 1,000 pounds of steam. . .53,300,000 foot pounds 

[521] 



118 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

In a paper read before the American Water Works Associa- 
tion, Mr. D. W. Mead estimates the duty of an air lift plant 
for different types of compressors as follows, assuming the effi- 
ciency (based on I. H. P. in steam cylinder) of the air lift to 
vary from 15 to 25 per cent. 





Steam con- 


Duty, in million foot pounds with 


Type of Compressor 


sumption, 
pounds dry steam 




25 per cent. 




per I. H. P. 


15 per cent. 




efficiency 


efficiency 


Compound Corliss 










16 to 20 


19 to 30 


31 to 25 


Simple condensing Corliss 










22 to 28 


13 to 10 


22.5 to 18 


Simple Corliss 










35 to 40 


9.5 to 8.5 


14 to 12 


Well designed high pressure 








compressor 


40 to 60 


8.5 to 5 


12 to 8 


Small straight line 








compressor 


50 to 80 


6 to 4.5 


10 to 6 



[522] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



119 



CONCLUSION 

A comparison of the advantages and disadvantages of the 
air lift pump shows that there is a field of usefulness of suffi- 
cient magnitude to make it an important apparatus deserving 
of further theoretical and experimental study. From a study 
of the foregoing discussion and accompanying data, ideas in 
regard to improvement in the design will no doubt be sug- 
gested to the designer or experimenter. However, a full re- 
alization of the complexity of the action must be appreciated, 
as also the number of variables which enter into the problem. 
In order to facilitate the study of results, the variables which 
may affect a particular type and size of pump are again given at 
this place. They are (1) percentage of submergence, (2) lift, 
(3) discharge, (4) volume of air, (5) pressure of air. The 
conclusions which may justifiably be deduced from the "Wis- 
consin experiments are given below, and hold only for the 
particular type, size and length of pump on which the experi- 
ments were performed. The inference, however, may be drawn 
that these conclusions would hold for other types and sizes. 

(1) The central air tube pump has the greatest theoretical 
capacity for a given size of well. 

(2) The coefficient of pipe friction and slip decreases as the 
discharge increases, and decreases as the ratio of volume of air 
to volume of water increases. (See Fig. 20.) 

(3) The coefficient of pipe friction and slip varies with the 
length of pump, but seems to be independent of the percentage 
of submergence and of the lift. 

(4) The length of pump, the percentage of submergence, 
and therefore, the lift remaining constant, there is a definite 
quantity of air causing the maximum discharge. This quan- 
tity of air for maximum discharge, as also the ratio of volume 
of air to volume of water, differs for different percentages 
of submergence and lift, the length of the pump remaining 
constant. (See. Fig. 21.) 

(5) The length of pump remaining constant, the maximum 
output (e. g. foot gallons) occurs at about the same percent- 

[523] 



120 BULLETIN OF THE UNIVERSITY OP WISCONSIN 

age of submergence for all rates of air consumption, being at 
from 61 to 65 per cent, for the pump used in the Wisconsin 
experiments. At other submergences the output varies as the 
ordinates of a parabola having a vertical axis. Under these 
conditions the lift does not remain constant as the percentage 
of submergence varies. (See Figs. 23 and 24.) 

(6) The length of pump and percentage of submergence re- 
maining constant, and therefore constant lift, the efficiency 
increases as the input decreases, that is, the highest efficiencies 
are obtained at the lowest rates of pumping. (See Figs. 27, 
28, and 30.) 

(7) By varying the percentage of submergence, and there- 
fore the lift, the length of pump remaining constant, the maxi- 
mum efficiency is obtained at approximately 63 per cent, sub- 
mergence for all rates of input or discharge. (See Figs. 27, 
28, and 29.) 

(8) The lift remaining constant, the efficiency increases as 
the percentage of submergence increases, for all rates of input 
and all practical percentages of submergence. (See Figs. 30 
and 31.) 

(9) With the same size and type of pump, the percentage of 
submergence remaining constant, the efficiency increased as 
the lift increased for the small lifts experimented on, that is, 
up to about 24 feet. From a theoretical study, however, the 
indications are that a point will be reached from which the 
efficiency will decrease as the lift increases. (See Figs. 32, 
33 and 34.) 

(10) Other conditions remaining constant, there is no advan- 
tage to be gained by introducing compressed air above the 
surface of the water in the well. (See Figs. 35, 36, and 37.) 

(11) The type of the foot-piece lias very little effect on the 
efficiency of the pump, so long as the air is introduced in an 
efficient manner and the full cross sectional area of the educ- 
tion pipe is realized for the passage of the liquid. Anything 
in the shape of a nozzle to increase the kinetic energy of the 
air is detrimental. (See Figs. 38 and 39.) 

(12) A diverging outlet which will conserve the kinetic 
energy of the velocity head increases the efficiency. (See Fig. 
40.) " 

[524] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



121 



TABLE I 
Series I 
li inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in 
i ubic feet per second. 


Absolute piessure of 
air at g-ag-e, in pounds 
per square inch. 


Input, in foot pounds 
per second. 


Discharg-e of water, in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharg-e of water, in 
gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
li in. tail piece. 


Coefficient of slip and 
pipe friction . 




q 

a 


P 


1 

i 


w 

w 


q 

w 


q 

gr 


s 


h 

1 


1 

o 


e 


q 

a 

q w 


V 

i 


C 

P 


1 


.04407 


18.007 


21.843 


.5766 


.00923 


4.143 


43.77 


10.865 


6.265 


28 684 


4.775 


1.08 


.2199 


2 


.04429 


18.061 


22.222 


.5834 


.00933 


4.187 


44.39 


10.743 


6.2C8 


28.209 


4.747 


1.09 


.2200 


3 


. 18057 


19 . 104 


J-V/O . oou 


.6867 


01098 


4 928 


43 47 


10 923 


7.501 


6.921 


16.446 


1.29 




4 


.12338 


18.445 


64.830 


.7500 


.01200 


5.386 


43.26 


10.963 


8.222 


12.683 


10.282 


1.41 


.0788 


5 


.12004 


18.480 


63.570 


.7519 


.01203 


5.399 


43.26 


10.962 


8.242 


12.965 


9.979 


1.41 


.0822 


'€ 


.09154 


18.231 


45.860 


.7326 


.01172 


5.260 


42.50 


11.110 


8.139 


17.747 


7.811 


1.37 


.1-000 


7 


.06307 


18.213 


31.477 


.7194 


.01151 


5.166 


44.01 


10.817 


7.782 


24.723 


5.480 


1.35 


.1300 


8 


.03174 


18.182 


15.731 


.3068 


.00491 


2.204 


44.37 


10.748 


3.298 


20.961 


6.465 


0.58 


.7382 


9 


.04428 


18.388 


22.961 


.6745 


.01079 


4.843 


48.34 


9.982 


6.733 


29.325 


4.104 


1.27 


.1821 


10 


.05909 


18.609 


32.108 


.8333 


.01333 


5.984 


47.85 


10.076 


8.396 


26.150 


4.433 


1.56 


.1188 


11 


.07671 


18.554 


41.130 


.9091 


.01454 


6.526 


47.91 


10.064 


9.148 


22.243 


5.276 


1.70 


.0883 


12 


.09592 


18.657 


52.970 


.8969 


.01435 


6.441 


48.15 


10.018 


8.984 


16.962 


6.(85 


1.69 


.0810 


14 


.03910 


18.501 


21.173 


. .4934 


.00789 


3.541 


47.31 


10.180 


5.023 


23.724 


4.956 


0.93 


.3458 


15 


.08244 


18.664 


45.518 


.9259 


.01481 


6.647 


49.25 


9. £06 


9.079 


19.946 


5.567 


1.74 


.0863 


16 


.12004 


18.846 


74.540 


.8734 


.01397 


6.270 


48.57 


9.936 


8.678 


11.643 


9.308 


1.64 


.0384 


17 


.12377 


18.642 


68.110 


.7813 


.01250 


5.610 


47.73 


10.098 


7.890 


11.584 


9.901 


1.47 


.0802 


18 


.12160 


18.574 


67.140 


.8048 


.0128S 


5.781 


45.99 


10.435 


8.898 


12.508 


9.441 


1.51 


.0778 


19 


.11300 


18.552 


62.130 


.8214 


.01314 


5.897 


45.88 


10.456 


8.589 


13.825 


8.600 


1.54 


.0805 


20 


.09660 


18.581 


53.3C0 


.8830 


.01413 


6.342 


47.64 


10.116 


8.9S3 


16.760 


6.837 


1.66 


.0830 


21 


.08652 


18.480 


46.752 


.8715 


.01394 


6.257 


47.65 


10.114 


8.814 


18.854 


6.207 


1.63 


.0895 


22 


.07158 


18.451 


38.433 


.8772 


.01403 


6.297 


47.35 


10.172 


8.923 


23.220 


5.102 


1.64 


.0978 


23 


.05665 


18.511 


30.825 


.8584 


.01373 


6.163 


47.47 


10.150 


8.712 


28.264 


4.126 


1.61 


.1141 



[525] 



122 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

I 



Series I — Continued 
114 inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 




Number of run. 


Quantity of free air, in 
cubic feet per second, 


Absolute pressure of 
air at gage, in pounds 
' per square inch. 


Input, in foot pounds 
: per second. 


Discharge of water, in 
1 pounds per second. 


DischaTge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 


Output, in foot pounds 1 
per second. ! 


Efficiency, in per cent. 


Hatio of volume of air 
to volume of water. 


Velocity of water in a 
li in. tail piece. 


Coefficient of slip and 


! 

3 

; ■ 

3 
I 




^a 


Pg 


•i 


w 

w 






s 


h i 


i 


e 


^a 
^w 


v i 


C 

p 




24 


.05198 


18.414 


27.747 


.7722 


.01235 


5.543 


48.02 


10.042 


7.754 


27.945 


4.209 


1.46 


. 1396' 


25 


. 04198 


18.588 


23.245 


.7649 


.01224 


5.494 


47.12 


10'. 216 


7.814 


33.618 


3.430 


1.43 


.15611 


26 


.02961 


18.628 


16.509 


.4838 


.00774 


3.474 


47.49 


10.146 


4.908 


29.731 


3.826 


0.90 


.4143- 


27 


.13172 


18.306 


69.660 


.6757 


.01081 


4.852 


41.15 


11.370 


7.682 


11.027 


12.185 


1.27 


.0857. 


28 


.10438 


18.019 


51.660 


.6612 


.01059 


4.753 


41.20 


11.360 


7.511 


14.540 


9.857 


1.24 


.1020.' 


29 


.08644 


17.917 


41.755 


.6678 


.01068 


4.793 


41.20 


11.360 


7.586 


18.168 


8.094 


1.26 


.1138! 


SO 


.07118 


17.840 


33.710 


.6601 


.01056 


4.739 


41.20 


11.360 


7.498 


22.243 


6.741 


1.24 


.128$ 


31 


.05195 


17.845 


24.597 


.6289 


.01006 


4.515 


41.22 


11.356 


7.142 


29.036 


5.1C4 


1.18 


.162® 


32 


.03002 


18.075 


15.075 


.4926 


.00788 


3.537 


41.23 


11.354 


5.592 


37.103 


3.810 


0.93 


.3185 


33 


.04664 


17.954 


22.707 


.6411 


.01026 


4.605 


41.20 


11.360 


7.283 


32.075 


4.546 


1.21 


.16 


898 


34 


.04134 


18.032 


20.524 


.5899 


.00944 


4.237 


41.25 


11.350 


6.695 


32.622 


4.379 


1.10 


.211$ 


35 


.13191 


19.009 


78.380 


.9389 


.01502 


6.741 


49.46 


9.765 


9.168 


11.697 


8.782 


1.76 


.0636 


36 


.10667 


18.411 


56.170 


.7859 


.01257 


5.642 


49.73 


9.712 


7.633 


13.588 


8.486 


1.48 


.09 


05 


37 


.08281 


18.505 


44.525 


.8696 


.01391 


6.243 


48.08 


10.030 


8.722 


19.590 


5.953 


1.63 


.091i' 


38 


.06049 


18.560 


32.893 


.8753 


.01400 


6.283 


48.23 


10.002 


8.754 


26.615 


4.321 


1.64 


.107; 


39 


.05265 


18.495 


28.226 


.7663 


.01226 


5.503 


49.12 


9.830 


7.532 


26.686 


4.294 


1.44 


.143, 


40 


.04789 


18.628 


26.405 


0.7519 


.01203 


5.399 


48.96 


9.862 


7.416 


28.087 


3.981 


1.41 


.157* 


41 


.12336 


18.502 


66.320 


0.6359 


.01017 


4.564 


48.41 


9.968 


6.339 


9.559 


12.130 


1.20 


.105] 


42 


.11095 


19.155 


67.730 


1.0498 


.01680 


7.541 


53.58 


8.968 


9.414 


13.899 


6.C03 


1.97 


.0^4* 


43 


.0912? 


19.068 


54.830 


1.0811 


.0173C 


7.765 


53.29 


9.022 


9.753 


17.789 


5.274 


2.03 


.071: 


44 


.0808f 


19.098 


48.752' 1.1237 


.01798 


8.07C 


54. 4C 


8.81C 


9.900 


20.307 


4.497 


2.11 


.0" 


2:i 



[526] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



123 



Series I — Continued 
1*4 inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


1 Quantity of free air, in 
I cubic feet per second. 


. 

Jl a O 
on - 

s o> 

(D rf c3 

■2 *^ ~ 

03 « 


Input, in footpounds 
per second. 


Discharge of water, in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge, of water, in 
gallons per minute. 


Submergence, in 
per cent. 


1 

Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
j li in. tail piece. 


Coefficient of slip and 
pipe friction. 




<*a 


Per 
» 




w w 




% 




s 


\ 


l O 


e 


^a 

q w 


v i 


C 

P 


45 


.07195 


19.071 


43.245 


1.1080 


.01773 


7.957 


54.38 


8.814 


9.766 


22.584 


4.058 


2.08 


.0782. 


46 


.06109 


19.070 


36.715 


1.1049 


.01768 


7.935 


54.72 


8.748 


9.666 


26.327 


3.456 


2.08 


.0831 


47 


.04831 


18.989 


28.573 


1.0102 


.01616 


7.253 


53.96 


8.894 


8.984 


31.443 


2.989 


1.90 


.1022 


48 


.03775 


18.919 


22.055 


0.7533 


.01205 


5.408 


53.64 


8.950 


6.742 


30.571 


3.133 


1.42 


.1886 


49 


.09612 


19.193 


59.790 


1.2658 


.02025 


9.089 


58.06 


8.102 


10.255 


17.152 


4.747 


2.38 


.0557 


50 


.08354 


19.202 


52.130 


1.2780 


.02045 


9.178 


58.20 


8.076 


10.321 


19.800 


4.085 


2.41 


.0596- 


51 


.08096 


19.203 


50.510 


1.2423 


.01988 


8.923 


58.18 


8.080 


10.037 


19.873 


4.073 


2.34 


.0642 


52 


.06112 


19.206 


38.137 


1.2384 


.01981 


8.891 


58.43 


8.032 


9.946 


26.083 


3.085 


2.32 


.0723 


53 


.05291 


19.206 


33.013 


1.1662 


.01866 


8.375 


58.21 


8.074 


9.415 


28.523 


2.836 


2.19 


.0841 


54 


.04347 


19.212 


27.158 


1.0928 


.01748 


7.845 


57.96 


8.122 


8.875 


32.680 


2.487 


2.05 


.0981 


55 


.03097 


19.213 


19.347 


0.8429 


.01349 


6.055 


57.84 


8.144 


6.864 


35.479 


2.296 


1.58 


.1727 


56 


.10173 


17.312 


56.050 


0.5690 


.00910 


4.084 


38.01 


11.976 


6.815 


12.158 


11. ISO 


1.07 


.1016 


57 


.09045 


17.382 


38.823 


0.6678 


.01068 


4.794 


39.24 


11.738 


7.83 r » 


20.193 


8.4(19 


1.26 


.0900 


58 


.08222 


17.378 


35.286 


0.5031 


.00805 


3.613 


38.76 


11.832 


5.952 


16.868 


10.214 


0.95 


.1526 


59 


.06988 


17.383 


29.994 


0.4949 


.00792 


3.555 


38.74 


11.836 


5.857 


19.526 


8.823 


0.93 


.1780 


60 


.06207 


17.383 


26.641 


0.4969 


.00795 


3.568 


38.77 


11.830 


5.878 


22.085 


7.808 


0.94 


.1901 


61 


.04920 


17.384 


21.117 


0.5015 


.00804 


3.C08 


38.82 


11.820 


5.939 


28.127 


6.120 


0.94 


.2113 


62 


.04412 


17.384 


18.937 


0.4587 


.00734 


3.294 


38.87 


11.810 


5.417 


28.605 


6.011 


0.86 


.2598 


63 


.05371 


17.384 


23.053 


0.4926 


.00788 


3.537 


38.93 


11.798 


5.812 


25.212 


6.816 


0.93 


.2137 


64 


.04413 


17.384 


20.065 


0.4926 


.00788 


3.537 


39.00 


11.786 


5.806 


28.937 


5.601 


2.93 


.2778- 


65 


.07917 


19.844 


55.450 


1.4286 


.02286 


10.260 


63.77 


7.000 


10.000 


18.035 


3.463 




.0613 



[527] 



124 



BULLETIN OP THE UNIVERSITY OF WISCONSIN 



Series I — Continued 
1% inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in 
cubic feet per second. 


Absolute pres3ure of 
air at gage, in pounds 
1 per square inch. 


Input, in foot pounds 
1 per second. 


Discharge of water, in 
pounds per second. 


Discharge of water' in 
cubic feet per second, 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
li in. tail piece. 


Coefficient of slip and 
pipe friction. 




% 


Pg 


ii 


w 


*W 


% 


s 


h i 


] o 


e 


i* 
^w 


v l 


C 

P 


66 


.07067 


19.592 


47.600 


1.4494 


.02319 


10.408 


63.67 


7.022 


10.177 


21.380 


3.048 


2.72 


.0586 


67 


.11658 


20.108 


84.090 


1.4337 


.02294 


10.296 


63.78 


6.997 


10.032 


11.930 


5.082 


2.69 


.0498 


68 


.09816 


19.964 


69.200 


1.4337 


.02294 


10.296 


63.68 


7.017 


10.060 


14.537 


4.279 


2.69 


.0545 


69 


.09712 


19.905 


67.940 


1.4388 


.02304 


10.341 


63.06 


7.136 


10.266 


15.113 


4.215 


2.70 


.0536 


70 


.09265 


19.823 


64.000 


1.4236 


.02278 


10.224 


64.80 


6.800 


9.680 


15.126 


4.067 


2.68 


.0558 


71 


.08114 


19.771 


55.590 


1.4184 


.02269 


10.184 


64.82 


6.798 


9.642 


17.345 


3.576 


2.66 


.0601 


72 


.08055 


19.764 


55.180 


1.4337 


.02294 


10.296 


62.12 


7.318 


10.491 


19.013 


3.511 


2.69 


.0576 


73 


.07391 


19.742 


50.410 


1.4286 


.02286 


10.260 


62.72 


7.202 


10.288 


20.410 


3.233 


2.69 


.0602 


74 


.06245 


19.677 


42.118 


1.4235 


.02278 


10.224 


62.55 


7.235 


10.299 


24.453 


2.742 


2.68 


.0825 


75 


.05394 


19.702 


36.580 


1.4036 


.02246 


10.081 


62.48 


7.250 


10.176 


27.820 


2.402 


2.64 


.0662 


76 


.03148 


19.790 


21.626 


No 


water 




64.85 


6.792 




pumpe 


d 






77 


.12212 


20.165 


87.8'0 


1.4134 


.02261 


10.148 


63.55 


7.013 


9.9^4 


11.330 


5.401 


2.65 


.0489 


78 


.10305 


20.056 


72.950 


1.4036 


.02246 


10.081 


63.65 


7.023 


9.857 


13.537 


4.588 


2.64 


.0550 


79 


.08105 


19.838 


55.520 


1.4286 


.02286 


10.260 


63.80 


6.995 


9.993 


18.000 


3.546 


2.69 


.0586 


SO 


.09444 


20.373 


69.960 


1.4235 


.02278 


10.224 


63.84 


6.988 


9.947 


14.218 


4.146 


2.68 


.0611 


81 


.07146 


19.837 


48.947 


1.4084 


.02253 


10.112 


63.88 


6.978 


9.827 


20.077 


3.172 


2.64 


.0639 


82 


.06102 


19.783 


41.427 


1.4494 


.02319 


10.408 


63.93 


6.9~0 


10.103 


24.387 


2.631 


2.72 


.0621 


83 


.05726 


19.781 


38.878 


1.4286 


.02286 


10.260 


63.94 


6.968 


9.954 


25.604 


2.505 


2.69 


.0646 


84 


.04501 


19.783 


30.559 


1.3888 


.02222 


9.973 


63.99 


6.958 


9.663 


31.620 


2.026 


2.61 


.0694 


85 


.02858 


19.849 


19.633 


1.2196 


.01951 


8.757 


63.90 


6.975 


8.507 


43.333 


1.465 


2.29 


.0848 


86 


. 03994 | 


19.827 


27.360 


1.3559 


.02169) 


9.735 


63.86 


6.983 


9.468 


34.606 


1.842 


2.55 


.0731 



[528] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



125 



Series I — Continued 
1^4 inch Harris Pump 
Length of Eduction Pipe 19.32 feet 





2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in 
cubic feet per second. 


Absolute pressure of 
air at gagp, in pounds 
per square inch. 


Input, in foot pounds 
per second. 


Discharge of water, in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. I 


Output, in foot pounds J 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
li In. tail piece. 


Coefficient of slip and 
pipe friction. 






Pg 


] i 


w w 


q w 


% 


s 


h l 


l o 


e 


% 

q w 


v i 


c 

p 


87 


.12640 


20.499 


97.310 


1.5564 


.02490 


11.175 


68.30 


6.125 


9.533 


9.797 


5.077 


2.92 


.0450 


88 


.11485 


20.354 


86.570 


1.5504 


.02481 


11.135 


68.08 


6.168 


9.563 


11.046 


4.629 


2.91 


.0477 


89 


.10194 


20.284 


76.210 


1.5444 


.02471 


11.090 


68.00 


6.183 


9.549 


12.530 


4.126 


2.90 


.0517 


90 


.06883 


20.236 


51.100 


1.6001 


.02560 


11.490 


67.88 


6.205 


9.928 


19.429 


2.689 


3.01 


.0581 


91 


.08070 


20.184 


59.440 


1.6065 


.02570 


11.534 


68.21 


6.142 


9.866 


16.597 


3.140 


3.02 


.0536 


92 


.07168 


20.046 


51.840 


1.5936 


.02550 


11.445 


68.22 


6.140 


9.784 


18.874 


2.811 


2.99 


.0555 


93 


.14772 


21.011 


120.840 


1.5936 


.02550 


11.445 


70.30 


5.738 


9.144 


7.567 


5.793 


2.99 




94 


.10643 


20.678 


83.390 


1.5936 


.02550 


11.445 


68.06 


6.172 


9.835 


11.793 


4.174 


2.99 


.0508 


95 


.09305 


20.517 


71.350 


1.6130 


.02581 


11.584 


67.94 


6.195 


9.992 


14.005 


3.606 


3.03 


.0524 


96 


.07808 


20.351 


58.560 


1.6265 


.02602 


11.678 


67.44 


6.290 


10.230 


17.470 


3.001 


3.05 


.0540 


97 


.07172 


20.368 


53.890 


1.7167 


.02747 


12.328 


71.20 


5.566 


9.554 


17.729 


2.612 


3.23 


.0515 


98 


.07137 


20.264 


52.820 


1.5747 


.02519 


11.306 


70.16 


5.765 


9.077 


17.185 


2.833 


2.96 


.0602 


99 


.06761 


20.386 


50.970 


1.6461 


.02634 


11.822 


68.23 


6.138 


10.104 


19.825 


2.567 


3.09 


.0563 


100 


.05948 


20.273 


44.108 


1.6461 


.02634 


11.822 


68.70 


6.048 


9.955 


22.570 


2.258 


3.09 


.0566 


101 


.05053 


20.252 


37.372 


1.5936 


.02550 


11.445 


68.87 


6.015 


9.585 


25.648 


1.982 


2.99 


.0618 


102 


.03959 


20.252 


29.282 


1.5094 


.02415 


10.838 


69.26 


5.940 


8.965 


30.617 


1.639 


2.84 


.0695 


103 


.02760 


20.230 


20.360 


1.1155 


.01785 


8.011 


69.10 


5.970 


6.659 


32.707 


1.546 


2.10 


.1360 


104 


.00707 


20.620 


5.425 


No 


water 




85.71 


2.751 




pumpe 


d 






105 


.00221 


20.356 


1.634 








69.56 


5.882 












106 


.02240 


15.217 


2.823 








24.87 


14.514 












107 


.02240 


16.134 


5.551 








25.40 


14.412 




<« 









[529] 



126 



BULLETIN OF THE 



UNIVERSITY 



OF WISCONSIN 



Series I — Continued 
1*4 inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in 
cubis feet per second. 


Absolute pressure of 
air at gage, in pounds 
per square inch. 


Input, in foot pounds 
per second. 


Discharge of water, in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 
1 per cent. 


Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
li in. tail piece. 


Coefficient of slip and 
pipe friction. 




^a 


Pa- 


lo 


w 

w 






s 


hi 


] o 


e 




v i 


C I 














P 


108 


.01307 


17.106 


4.848 


No 


water 




31.18 


13.296 




pumpe 


d 






109 


.00697 


17.934 


3.284 


« 


'< 




41.54 


11.294 












110 


.00216 


20.350 


1.595 








70.30 


5.738 




<< 








111 


.00857 


17.501 


3.600 








41.03 


11.394 












112 


.00428 


19.178 


2.621 








51.45 


9.380 












113 


.00426 


19.120 


2.585 








58.25 


8.064 












114 


.00679 


18.478 


3.628 








46.37 


10.362 












115 


.00212 


19.455 


1.363 








62.00 


7.342 












116 


.10044 


20.930 


81.390 


1.8348 


.02935 


13.173 


V4.90 


4.850 


8.898 


10.933 


3.422 


3.45 


.04iJ 


117 


.10294 


20.920 


83.330 


1.8264 


.02922 


13.114 


75.00 


4.830 


8.821 


10.585 


3.523 


3.43 


.045! 


118 


.09423 


20.852 


75.570 


1.8518 


.02962 


13.294 


74.92 


4.846 


8.973 


11.875 


3.181 


3.48 


.04$ 


119 


.08458 


20.814 


67.510 


1.8692 


.02991 


13.424 


74.88 


4.852 


9.069 


13.433 


2.828 


3.52 


.041 


120 


.07523 


20.794 


59.930 


1.8780 


.03005 


13.487 


74.91 


4.848 


9.104 


15.192 


2.504 


3.54 


.04: 


121 


.06751 


20.776 


53.670 


1.8780 


.03005 


13.487 


74.88 


4.852 


9.112 


16.978 


2.247 


3.54 


.04 


122 


.05883 


20.677 


46.145 


1.8868 


.03019 


13.550 


74.77 


4.874 


9.196 


19.928 


1.949 


3.55 


.Offl 


123 


.04866 


20.679 


38.203 


1.8517 


.02962 


13.294 


74.84 


4.860 


8.999 


23.558 


1.643 


3.48 


.08 


124 


.03660 


20.677 


28.708 


1.7544 


.02807 


12.598 


75.15 


4.800 


8.421 


29.335 


1.304 


3.30 


.0' 


125 


.04616 


20.584 


35.817 


1.8100 


.02896 


12.997 


74.66 


4.894 


8.857 


24.727 


1.594 


3.41 




126 


.02924 


20.580 


29.666 


1.5152 


.02424 


10.879 


75.13 


4.804 


7.279 


24.535 


1.20" 


2.81 


.o:- 


127 


.05779 


20.588 


44.885 


1.8517 


.02962 


13.294 


74.59 


4.910 


9.092 


20.256 


1.951 


3.48 


.01 


128 


.06459 


20.643 


50.460 


1.8692 


.02991 


13.424 


74.50 


4.926 


9.208 


18.250 


2. ICO 


3.52 


.0 



[530] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



127 



Series I — Continued 
114 inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



4 


5 


6 


7 


m 


c 




q 


)t pound: 


r water, i 
second. 


f water, i 
>er secon 


! water, i 
minute. 


&i 

a 


si 






•rH y 

* CB 


Dischai 
pound; 


Dischai 
cubic 1 


Dischai 
g-allon: 


h 




q w 





- . 

-• o 
O 



5? a; 1 
Q bi : 

0^ : 



02 



PS 

o 
» 

o 

o . 



2| 

Jo 

O <D 



129 1 


.08207 


20.718: 


64.750 


1.8692 


.02991 


13.424 


74.54 


4.918 


9.193 


14.197 


2.744 


3.52 


130 


.01955 


20.680 


15.365 


No 


water 




75.15 


4.800 




pumpe 


d 




131 


.11572 


20.746 


91.560 


1.9513 


.03122 


14.013 


79.93 


3.878 


7.567 


8.264 


3.707 


3.67 


132 


.10184 


20.753 


80.660 


1.9902 


.03184 


14.292 


80.00 


3.864 


7.690 


9.534 


3.199 


3.74 


133 


.09086 


20.764 


72.030 


2.0409 


.03265 


14.654 


80.14 


3.836 


7.828 


10.868 


2.783 


3.84 


134 


.14397 


21.580 


123.820 


1.9325 


.03092 


13.877 


80.55 


3.758 


7.262 


5.865 


4.657 


3.63 


135 


.13171 


21.575 


113.170 


1.9418 


.03107 


13.944 


79.84 


3.896 


7.565 


6.685 


4.240 


3.66 


136 


.10076 


21.400 


84.870 


2.0000 


.03200 


14.362 


79.55 


3.950 


7.900 


9.308 


3.149 


3.76 


137 


.08777 


21.000 


70.450 


2.0305 


.03248 


14.577 


79.55 


3.950 


8.020 


11.383 


2.702 


3.82 


138 


.08420 


21.248 


69.640 


2.0513 


.03282 


14.730 


79.45 


3.970 


8.143 


11.693 


2.566 


3.85 


139 


.07495 


21.196 


61.650 


2.0513 


.03282 


14.730 


79.52 


3.958 


8.119 


13.170 


2.284 


3.85 


140 


.07439 


21.193 


61.140 


2.0620 


.03299 


14.806 


79.52 


3.958 


8.161 


13.348 


2.255 


3.88 


141 


.06756 


21.188 


55.470 


2.0833 


.03333 


14.958 


79.54 


3.954 


8.237 


14.830 


2.027 


3.91 


142 


.06330 


21.184 


51.970 


2.0726 


.03316 


14.883 


79.78 


3.908 


8.099 


15.583 


1.909 


3. £0 


143 


.05553 


21.162 


45.421 


2.0833 


.03333 


14.958 


79.72 


3.918 


8.162 


17.970 


1.666 


3.91 


144 


.05171 


21.067 


42.335 


1.9763 


.03162 


14.192 


78.93 


4.070 


8.043 


19.000 


1.635 


3.71 


145 


.04637 


21.071 


38.000 


1.9481 


.03117 


13.989 


79.11 


4.034 


7.858 


20.681 


1.488 


3.67 


146 


.04024 


21.004 


32.670 


1.8127 


.02900 


13.016 


78.22 


4.208 


7.627 


23.347 


1.388 


3.41 


147 


.02275 


21.003 


18.470 


1.6667 


.02668 


11.974 


79.19 


4.020 


6.700 


36.276 


0.853 


3.14 


148 


.00708 


21.034 


5.769 


No 


water 




79.06 


4.046 




pumpe 


d 




149 


.14084 


21.899 


126.830 


2.0000 


.03200 


14.363 


84.10 


3.072 


6.144 


4.845 


4.402 


3.70 



[531] 



128 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Series I — Continued 
114 inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



1 


2 


3 


4 


5 


6 

C!n-S 

„ a 

* CD 

0* 
cd a> 
tjj — 

0^ 




9 


10 


„ 


12 


13 


14 


Number of run. 


*Q J Quantity of free air, in 
p cubic feet per second. 


v 1 Absolute pressure of 
at! ! air at gage, in pounds 
! per square inch. 


1-1 Input, in foot pounds 1 
1 per second. I 


^ Discharge of water, in 
3 1 pounds per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


, Lift, in feet. 


Output, in foot pounds 
; per second. 


Efficiency, in per cent. 


Ratio of volume of air 
! to volume of water. 


Velocity of water in a 
li in. tail piece. 


Coefficient of slip and 
pipe friction. 


q w 


% 


s 


h 


] o 


e 


%y 


v i 


c 

p 


150 


.13687 


1 

21.874 


123.020 


2.0135 


.03221 


14.456 


84.27 


3.040 


6.121 


4.976 


4.250 


3.78 


.0355 


151 


.12498 


21.853 


111.860 


2.0340 


.03254 


14.605 


83.95 


3.100 


6.305 


5.637 


3.841 


3.82 


.0375 


152 


.11500 


21.781 


102.330 


2.0691 


.03310 


14.856 


83.90 


3.110 


6.435 


6.288 


3.474 


3.89 


.0382 


153 


.10738 


21.749 


95.130 


2.1127 


.03380 


15.170 


84.50 


2.994 


6.325 


6.649 


3.177 


3.97 


.0384 


154 


.10107 


21.528 


88.600 


2.1277 


.03403 


15.228 


84.28 


3.038 


6.464 


7.296 


2.970 


3.99 


.0386 


155 


.09155 


21.483 


79.850 


2.1584 


.03453 


15.497 


84.18 


3.056 


6.596 


8.261 


2.651 


4.05 


.0393 


156 


.08325 


21.466 


72.540 


2.1819 


.03491 


15.667 


84.44 


3.006 


6.558 


9.041 


2.385 


4.10 


.0403 


157 


.08042 


21.436 


69.770 


2.2060 


.03529 


15.838 


84.39 


3.014 


6.649 


9.530 


2.279 


4.15 


.0397 


158 


.07755 


21.414 


67.110 


2.2142 


.03542 


15.897 


84.33 


3.028 


6.704 


9.989 


2.189 


4.16 


.0398 


159 


.07085 


21.385 


61.090 


2.2223 


.03556 


15.960 


84.28 


3.038 


6.751 


11.053 


1.992 


4.18 


.0404 


160 


.06289 


21.375 


54.170 


2.2389 


.03582 


16.077 


84.47 


3.000 


6.716 


12.397 


1.756 


4.21 


.0411 


161 


.05470 


21.353 


46.913 


2.2223 


.03556 


15.960 


84.56 


2.984 


6.631 


14.135 


1.538 


4.18 


.0424 


162 


.05888 


21.353 


50.500 


2.2223 


.03556 


15.960 


84.40 


3.014 


6.69S 


13.264 


1.656 


4.18 


.0420 


163 


.04977 


21.328 


42.610 


2.1740 


.03478 


15.610 


84.43 


3.008 


6.539 


15.346 


1.431 


4.0S 


.0462 


164 


.03899 


21.315 


33.320 


2.1054 


.03368 


15.116 


84.44 


3.006 


6.329 


18.995 


1.158 


3.96 


.0477 


165 


.03178 


21.322 


27.187 


1.7753 


.02840 


12.746 


84.37 


3.020 


5.361 


19.720 


1.119 


3.34 


.0716 


166 


.00215 


21.535 


1.885 


NO 


water 




85.04 


2.890 




pumpe 


d 






167 


.14682 


22.350 


140.500 


2.1899 


.03503 


15.722 


90.29 


1.876 


4.10S 


2.924 


4.192 


4.11 




168 


.11795 


22.135 


110.440 


2.3077 


.03692 


16.570 


90.21 


1.892 


4.366 


3.953 


3.195 


4.33 


.0336 


169 


.13497 


22.305 


128.640 


2.2815 


.03650 


16.382 


91.02 


1.736 


3.961 


3.079 


3.698 


4.28 


.0317 


170 


.13884 


22.324 


132.440 


2.2389 


.03582 


16.077 


90.31 


1.872 


4.191 


3.165 


3.876 


4.21 


.0322 



[532] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



129 



Series I — Continued 
1% inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in 
cubic feet per second. 


Absolute pressure of air 
at gage, in pounds per 
square inch. 


Input, in foot pounds 
per second. 


Discharge of water, in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. j 


Velocity of water in a 
H in. tail piece. 


Coefficient of slip and 
pipe friction. 




\ 




1 

i 


W 

w 




% 


S 


h 

i 


1 

o 


e 


q w 


V 

i 


c 

p 


171 


12436 


22.172 


116.740 


2.2729 


.03636 


16.319 


90.06 


1.920 


4.364 


3.738 


3.421 


4.27 


.0334 


172 


.11134 


22.078 


103.670 


2.3167 


.03706 


16.633 


90.10 


1.912 


4.429 


4.273 


3.004 


4.35 


.0344 


173 


.10229 


22.019 


94.450 


2.3623 


.03780 


16.965 


90.09 


1.916 


4.526 


4.792 


2.706 


4.44 


.0346 


174 


.09712 


21.975 


89.450 


2.3810 


.03809 


17.095 


89.96 


1.940 


4.619 


5.164 


2.550 


4.47 


.0348 


175 


.08709 


21.918 


79.540 


2.4097 


.03855 


17.302 


89.78 


1.974 


4.757 


5.980 


2.259 


4.53 




176 


.07804 


21.886 


71.170 


2.4491 


.03918 


17.584 


89.78 


1.974 


4.835 


6.793 


1.992 


4.60 




177 


.07448 


21.872 


67.870 


2.4692 


.03951 


17.733 


89.86 


1.960 


4.840 


7.130 


1.885 


4.64 




178 


.06739 


21.856 


61.200 


2.4692 


.03951 


17.733 


89.80 


1.970 


4.864 


7.948 


1.706 


4.64 




179 


.06334 


21.859 


57.850 


2.4794 


.03967 


17.805 


90.34 


1.868 


4.631 


8.006 


1.597 


4.66 




180 


.05520 


21.837 


50.340 


2.4592 


.03935 


17.661 


90.32 


1.870 


4.599 


9.135 


1.403 


4.63 




181 


.05963 


21.840 


54.380 


2.4692 


.03951 


17.733 


90.43 


1.850 


4.568 


8.400 


1.509 


4.64 




182 


.04527 


21.831 


41.215 


2.4195 


.03871 


17.373 


90.32 


1.870 


4.524 


10.977 


1.170 


4.54 




183 


.03220 


21.823 


29.290 


2.1353 


.03416 


15.332 


89.72 


1.986 


4.241 


14.478 


0.943 


4.02 


.0536 


184 


.03905 


21.753 


35.252 


2.2814 


.03650 


16.382 


88.99 


2.126 


4.850 


13.759 


1.070 


4.28 


.0454 


185 


.00218 


21.774 


1.971 


No 


water 




89.67 


1.996 




pumpe 


d 






186 


.13092 


22.648 


129.490 


2.4002 


.03840 


17.234 


95.63 


0.844 


2.026 


1.564 


3.410 


4.51 




187 


.12525 


22.595 


123.300 


2.4194 


.03871 


17.373 


95.65 


O.840 


2.032 


1.648 


3.236 


4.55 




188 


.11753 


22.52S 


114. 90C 


2.4491 


.03918 


17.584 


95.55 


0.860 


2.106 


1.832 


3.000 


4.60 




189 


.10805 


22.45S 


104. 96C 


2.4897 


.03985 


17.876 


95.47 


0.874 


2.176 


2.072 


2.713 


4.67 




190 


.1003S 


22.385 


96.90C 


2.5106 


.04017 


18.028 


95.44 


0.880 


2.208 


2.28C 


2.49S 


4.72 




191 


.09305 


22.33J 


89.30( 


► 2.553S 


.0408J 


18.334 


95.3" 


0.894 


2.28S 


2.55C 


2.277| 4.80 





P [533] 



130 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Series I — Continued 
114 inch Harris Pump 
Lengtn of Eduction Pipe 19.32 feet 



.Bra 

.a o 

03 w 
03 

«h £ 
o 

>S 03 

£ O 

s§ 



a; o 

ft »J3 

Ec a o 

pH 03 03 

CD 03 



^ a 
.3 8 



a id 



O 2 

t» o 



si 



OP 



OS 

pic 



.5 

03 
O 

a 

03 • 

03 



10 



12 



O 03 
cS O 



192 


.09000 


22.377 


86.810 


2.5643 


.04103 


193 


.08445 


22.327 


80.940 


2.5974 


.04156 


194 


.07875 


22.306 


75.360 


2.6549 


.04248 


195 


.07531 


22.283 


71.900 


2.6202 


.04192 


196 


.06806 


22.255 


64.770 


2.6433 


.04229 


197 


.06359 


22.230 


60.420 


2.6549 


.04248 


198 


.05979 


22.213 


56.720 


2.6667 


.04266 


199 


.05071 


22.203 


48.020 


2.6667 


.04266 


200 


.04565 


22.187 


43.200 


2.6549 


.04248 


201 


.03973 


22.185 


37.597 


2.6088 


.04174 


202 


.02253 


22.210 


21.353 


2.4794 


.03967 


203 


.00221 


22.284 


21.114 


No 


water 


204 


.12955 


23.034 


132.370 


2.5237 


.04038 


205 


.12427 


23.007 


126.890 


2.5237 


.04038 


206 


.11348 


22.954 


115.090 


2.5642 


.04103 


207 


.10414 


22.833 


104.580 


2.6060 


.04161 


208 


.10875 


22.832 


109.230 


2.5974 


.04156 


209 


.09923 


22.821 


99.520 


2.6231 


.04197 


210 


.08862 


22.779 


88.600 


2.6846 


.04295 


211 


.09365 


22.781 


93.700 


2.6490 


.04238 


212 


.08556 


22.773 


85.480 


2.7027 


.04324 



18.414 

18.653 
19.066 
18.814 
18.982 
19.066 
19.147 
19.147 
19.066 
18.733 
17.805 

18.123 
18.123 
18.415 
18.674 
18.652 
18.837 
19.277 
19.021 
19.406 



95.60 
95.48 
95.47 
95.39 
95.38 
95.44 
95.30 
95.34 
95.42 
95.50 
95.96 
94.36 
100. L9 
100.35 
100.23 
100.02 
100.02 
99.96 
99.70 
99.74 
99.69 



0.850 
0.872 
0.874 
0.890 
0.892 
0.880 
0.908 
0.900 
0.884 
0.870 
0.780 
1.090 
—0.054 
— 
—0.046 
—0.002 
—0.002 
+0.006 
+ 0.05S 
+ 0.050 
+0.060 



2.180 


2.511 


2.194 


4.82 


2.265 


2.798 


2.032 


4.89 


2.320 


3.079 


1.854 


4.98 


2.332 


3.244 


1.796 


4.92 


2.358 


3.641 


1.609 


4.97 


2.336 


3.867 


1.497 


4.98 


2.421 


4.269 


1.402 


5.01 


2.400 


4.998 


1.189 


5.01 


2.347 


5.433 


1.075 


4.98 


2.270 


6.036 


0.952 


4.90 


1.934 


9.057 


0.568 


4.66 




pumpe 


d 








3.209 


4.74 






3.078 


4.74 






2.766 


4.81 






2.503 


4.89 






2.617 


4.89 


0.016 


0.000 


2.364 


4.93 


0.156 


0.002 


2.063 


5.04 


0.133 


0.C01 


2.210 


4.97 


0.162 


0.002 


1.979 


5.08 



[534] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



131 



Series I — Continued 
114 inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



© 02 

Sh 03 



3* 



i.s§ 

^ © 

rn 

ho 3 

3+- O 1 



o . 

n o 
— o 

. (D 

a a) 
c a 



4) C 



0) Q 

■*= s 

o 3 

w o 

S a 



*a 

52 

o to 



03 03 
£ ° 

DO 



9 


10 




spun* 




a 


: in feet. 


put in foot 
? second. 


«H 


3 4> 


h l 





<H 03 
O 03 
o3 O 



i w 



213 


.08246 


22.733 


75.770 


2.7211 


.04354 


19.542 


99.62 


+0.072 


214 


.07269 


22.709 


66.680 


2.7492 


.04399 


19.743 


99.54 


+0.088 


215 


.06837 


22.679 


67.780 


2.7683 


.04429 


19.878 


99.50 


+0.096 


216 


.06458 


22.669 


63.970 


2.7779 


.04444 


19.945 


99.48 


+0.100 


217 


.06021 


22.657 


59.460 


2.8270 


.04523 


20.300 


99.95 


+0.010 


218 


.05598 


22.654 


55.280 


2.8270 


.04523 


20.300 


99.99 


+0.002 


219 


.03971 


22.633 


39.155 


2.8270 


.04523 


20.300 


99.95 


+0.O10 


219% 


.04560 


22.203 


43.115 


2.8471 


.04555 


20.443 


100.03 


—0.006 


220 


.03271 


22.191 


30.905 


2.7875 


.04460 


20.017 


100.31 


—0.060 


221 


.02280 


22.178 


21.525 


2.5642 


.04103 


18.414 


99.96 


+0.008 


222 


.12788 


23.403 


135.060 


2.6471 


.04235 


19.007 


105.21 


—1.008 


223 


.12374 


22.377 


130.420 


2.6666 


.04266 


19.147 


105.11 


—0.988 


224 


.11073 


23.309 


116.030 


2.7493 


.04399 


19.743 


105.25 


—1.014 


225 


.10584 


23.257 


110.340 


2.7682 


.04429 


19.878 


105.17 


—1.000 


226 


.10312 


23.234 


107.270 


2.7778 


.04444 


19.945 


105.06 


—0.978 


227 


.10031 


23.216 


104.270 


2.7973 


.04475 


20.084 


105.07 


—0.980 


228 


.09511 


23.188 


95.010 


2.8070 


.04491 


20.157 


105.06 


—0.978 


229 


.07579 


23.148 


78.320 


2.8470 


.04555 


20.443 


104.95 


—0.958 


230 


.08397 


23.121 


86.490 


2.8778 


.04104 


20.664 


104.92 


—0.950 

I?.,;'; f/j 


231 


.0£059 


23.087 


82.780 


2. 9] 99 


.04671 


20.964. 


105.05 


—0.974 


232 


.07440 


23.070 


76.380 


2.9521 


.04723 


21.19S 


105.09 


—0.982 



0.196 
0.242 
0.266 
0.278 
0.028 
0.006 
0.028 



0.021 



0.003 
0.004 
0.004 
O.004 
0.000 
0.000 
0.001 



0.C01 



1.894 
1.652 
1.544 
1.453 
1.331 
1.2E8 
0.878 
1.001 
0.733 

0. 556 
3.020 
2.901 
2.517 
2.390 
2.320 
2.242 
2.118 

1. C64 
1.824 
1.725 
1.575 



[535] 



132 



BULLETIN OF THE UNIVERSITY OP WISCONSIN 



Series I — Continued 
1% inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



d • 



o+-> 

Z. * 

>5 0) 



03 

o§ 

0) o 

vi G 
0> 

« 0> <D 

a &£ 

<v> c3 c3 
+S bs d 

d +j o 1 
-gos- 

CO h 

3* 



d O 
* o 

- OJ 

/: 

d t, 
a£ 
a a 



s8 



© Q 

,d d 
o P 

72 O 

£ a 



.5^ 

d 
t* o 

S ° 



2 O 

■§3 

CO 3 



<D Q, 

o3 



CD 

O 

s 

CD . 
© CD 

5 a 



10 



— S3 

o 

p 

Is 



233 


.06761 


23.044 


69.250 


2.9963 


.04794 


21.517 


105.17 


—1.000 


234 


.06339 


22.992 


64.630 


3.0304 


.04849 


21.763 


105.00 


—0.984 


235 


.05810 


22.929 


58.620 


3.0653 


.04904 


22.010 


105.42 


—1.048 


236 


.05008 


22.927 


50.520 


3.0890 


.04942 


22.180 


105.30 


—1.024 


237 


.04558 


22.923 


45.950 


3.0890 


.04942 


22.180 


105.33 


—1.030 


238 


.04068 


22.921 


41.010 


3.0890 


.04942 


22.180 


105.31 


—1.026 


239 


.03528 


22.919 


35.540 


3.0304 


.04849 


21.763 


105.26 


—1.016 


240 


.01998 


22.920 


20.128 


2.9413 


.04706 


21.121 


105.47 


—1.058 


241 


No 


air 




1.5504 


.02481 


11.135 


105.19 


—1.002 


242 


.13492 


23.512 


143.150 


2.8125 


.04500 


20.196 


111.07 


—2.140 


243 


.14263 


23.523 


151.430 


2.7610 


.04417 


19.824 


111.17 


—2.160 


244 


.12553 


23.861 


136.980 


2.8572 


.04572 


20.520 


110.95 


—2.116 


245 


.12973 


23.891 


141.970 


2.8214 


.04514 


20.260 


110.84 


—2.096 


246 


.11867 


23.801 


128.960 


2.8847 


.04615 


20.713 


110.69 


—2.064 


247 


.11115 


23.738 


120 200 


2.9127 


.04662 


20.923 


110.57 


—2.042 


248 


.10592 


23.684 


L13.970 


2.9317 


.04691 


21.054 


110.39 


—2.008 


249 


.09823 


23.638 


105.170 


2.9803 


.04769 


21.404 


110.35 


— 2.000 


250 


.08954 


23.521 


95.130 


3.0000 


.04800 


21.543 


109.56 


—1.848 


251 


.08043 


23.519 


85.390 


3.1142 


.04983 


22.364 


110.53 


—1.996 


252 


.07665 


23.489 


81.190 


3.1579 


.05052 


22.674 


110.14 


—1.960 


253 


.07263 


23.451 


76.660 


3.1690; .05070 


22.754 


110.14 


—1.960 



11 


12 


13 


14 


•ent. 


>f volume of air 
ime of water. 


83 

d 


-a 
d 


icy, in per c 


;y of water : 
;ail piece. 


ent of slip i 
"iction. 


Efficier 


' Ratio o 
to VOll 


Velocil 
li in. 1 


Coefflci 
pipe fi 


e 


q 

w 


V 

i 


c 

p 





































used 



















































1.410 
1.307 
1.185 
1.013 
0.922 
0.823 
0.728 
0.425 



2.746 
2.874 
2.572 
2.384 
2.258 
2.0C0 
1.866 
1.164 
1.517 
1.433 



[536] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



133 



Series I — Continued 
1% inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



1 


2 


3 


4 


5 


6 


7 


8 


9 


imber of run. 


antity of free air, in 1 
ibic feet per second. 


•solute pressure of 
r at gage, in pounds 
jr square inch. 


Input, in foot pounds 
per second. 


Discharge of water, in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


B 

© 
o 

© 

^ a 
S © 

a£ 

■9 s 


:t, in feet. 


i_> 
Z 






s a 






q 

a 


P 

g 


1 

i 


W 

w 


q 

w 


Q 

8 


s 


h 

1 


254 


.06489 


23.434 


68.440 


3.2143 


.05143 


23.081 


110.01 


— 1.934 


255 


.06090 


23.414 


64.050 


3.2493 


.05199 


23.333 


110.33 


—1.996 


256 


.05619 


23.390 


59.050 


3.2729 


.05233 


23.486 


109.71 


—1.878 


257 


.04621 


23.382 


48.530 


3.2848 


.05255 


23.585 


109.96 


—1.924 


258 


.03994 


23.374 


41.911 


3.2969 


.05275 


23.675 


110. 6 J 


—2.048 


259 


.03288 


23.390 


34.555 


3.2493 


.05199 


23.333 


110.96 


—2.116 


260 


.02289 


23.412 


23.902 


3.1036 


.04965 


22.284 


110.57 


—2.042 


261 


No 


air 




2.0980 


.03357 


15.066 


109.80 


—1.892 


262 


.12304 


24.287 


137.660 


3.0213 


.04834 


21.695 


116.03 


—3.098 


263 


.13075 


24.364 


147.180 


2.9852 


.04776 


21.435 


115.97 


—3.086 


264 


.11404 


24.235 


127.070 


3.0677 


.04908 


22.027 


115.81 


—3.056 


265 


.10711 


24.224 


119.200 


3.1057 


.04969 


22.303 


115.85 


—3.064 


266 


.09998 


24.161 


110.740 


3.1447 


.05031 


22.580 


115.76 


—3.026 


267 


.10022 


24.110 


110.520 


3.1849 


.05096 


22.872 


115.47 


—2.990 


268 


.08880 


24.024 


97.180 


3.2260 


.05162 


23.167 


115.33 


—2.962 


269 


.07680 


24.050 


84.340 


3.3115 


.05298 


23.778 


116.25 


—3.140 


270 


.07653 


24.040 


83.970 


3.3333 


.05333 


23.935 


116.06 


—3.102 


271 


.06921 


24.022 


75.750 


3.3785 


.05406 


24.263 


115.77 


—3.048 


272 


.06533 


24.019 


71.500 


3.4485 


.05517 


24.762 


115.94 


—3.080 


273 


.06115 


23.968 


66.680 


3.4604 


.05537 


24.851 


115.65 


—3.024 


274 


.05670 


23.958 


61.800 


3.4845 


.05575 


25.022 


115.61 


—3.018 



p 
o 
a 

t 
o 

a a 

■- 1 o 



o © 
> B 

o o 

03 O 



1w 

































used 



















































1.262 
1.171 
1.074 
0.879 
0.757 
0.633 
0.461 

2.545 
2.738 
2.324 
2.156 
1.987 
1.967 
1.720 
1.450 
1.435 
1.280 
1.184 
1.104 
1.017 



[537] 



134 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Seeies I — Continued 
114 inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



1 


2 


3 


4 


5 


6 




8 


9 


10 


11 


12 


13 


14 


i Number of run. 


Quantity of free air, in 
cubic feet per second. 


Absolute pressure of air 
at g-ag-e, in pounds per 
spuare inch. 


Input, in foot pounds 
per second. 


Dischafg-e of water, in 
pounds ppr second. 


1 

Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. j 

1 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
1 li in. tail piece. 


1 Coefficient of slip and 
pipe friction. 


1 


q 

a 


P 

S 


1 

i 


w 

w 


q 

w 


q . 


s 


h 

1 


1 




e 


^a 

q w 


v. 
i 


C 


275 
276 
277 
278 


.04641 
.04044 
.03309 
No 


23.922 
23.902 


50.400 
43.855 
35.840 


3.5090 


.05614 


25.197 


115.43 


—2.982 






0.827 


6.59 




3.5213 


: 05634 


25.286 


115.47 


—2.990 
—2.960 






0.718 


6.61 




23.881 
air 


3.5590 


.05694 


25.555 


115.33 






0.581 


6.68 




2.7550 


.04408 


19.783 


115.82 


—3.057 




used 


5.17 




306 


.12283 


17.824 


57.130 


0.4672 


.00762 


3.420 


35.75 


12.413 


5.911 


10.347 


16.220 


0.S9 


.12 13 


307 


.12272 


17.833 


57.360 


0.4793 


.00767 


3.442 


35.86 


12.392 


5.939 


10.354 


15. COO 


O.90 


.1241 


308 


.11278 


17.745 


51.420 


0.4793 


.00767 


3.442 


35.14 


12.532 


6.006 


11.680 


14.705 


0.90 


.1319 


309 


.09949 


17.617 


43.995 


0.4785 


.00766 


3.438 


35.09 


12.540 


6.000 


13.637 


12.930 


0.89 


.1480 


310 


.08357 


17.592 


36.955 


0.4793 


.00767 


3.442 


35.04 


12.550 


6,015 


16.277 


10.897 


0.90 


.1683 


311 


.09033 


17.595 


39.943 


0.4800 


.00768 


3.447 


34.81 


12.595 


6.045 


15.135 


11.763 


0.90 


a* 


312 


.07275 


17.579 


32.112 


O.4870 


.00779 


3.496 


35.28 


12.507 


6.092 


18.972 


9.339 


0.91 


.1120 


313 


.06595 


17.553 


28.860 


0.4796 


.00767 


3.442 


35.20 


12.520 


6. €04 


20.804 


8.599 


o.ro 


.1968 


314 


.05679 


17.514 


24.628 


0.4598 


.00736 


3.303 


35.22 


12.515 


5.754 


23.3C3 


7.716 


0.S7 


.2267 


315 


.05016 


17.494 


21.605 


0.4396 


.00703 


3.155 


35.44 


12.473 


5.484 


25.382 


7.135 


0.82 


.2593 


.316 


.0464£ 


17.608 


20.695 


0.4255 


.00681 


3.056 


35.74 


12.415 


5.283 


25.530 


6.825 


0.80 


1 .2981 


317 


.03816 


17.607 


16.992 


0.3643 


.005SS 


2.617 


35.87 


12.390 


4.514 


26.562 


6.545 


0.68 


.4215 


318 


.0329( 


) 17.601 


20.44: 


0.272." 


flfUSfi 1 957 


35.9: 


12.38C 


3.374 


16.504 


7.546 


0.51 




1 







[538] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



135 



Series 2 
l 1 /! inch Harris Pump 
Length of Eduction Pipe 19.32 feet 



"5 o 



+a 03 

Pi X 
CSS 
£^ 

Go 



o§ 

<D O 

tn $3 C 

<d „•« 

a. <b 

2< tL S- 

m & «s 



C 
E3 
O 

a 

n O 



a- q, 



^ CD 



5 3 
o ^ 



0) 

o 

© • 

is 

02 



10 



+3 

CD 
03 
=1— c 

.s 

3 



O 

o . 

S pi 



O <D 

%°> 

c5 O 



£ 6 

t>s"S 



14 



4^.2 

is 



319 


.06355 


17.457 


26.938 


0.3239 


.00518 


2.325 


30.00 


13.524 


4.381 


16.261 


320 


.05166 


21.501 


44.700 


2.1391 


.03*9.2 


15.356 


83.10 


3.265 


6.984 


15.622 


321 


.07371 


21.849 


66.320 


2.1506 


.03441 


15.445 


83.45 


3.198 


6.878 


10.370 


322 


.09043 


22.143 


83.910 


2.1040 


.03366 


15.108 


83.30 


3.226 


6.787 


8.088 


323 


.11443 


22.762 


112.790 


2.0202 


.03232 


14.506 


83.50 


3.188 


6.441 


5.711 


324 


.15172 


23.735 


162.980 


1.8958 


.03033 


13.613 


83.64 


3.162 


5.995 


3.678 


325 


.04865 


21.513 


42.093 


2.1740 


.03478 


15.612 


83.50 


3.188 


6.931 


16.466 


326 


.05167 


21.578 


45.090 


2.1666 


.03466 


15.558 


83.50 


3.188 


6.907 


15.318 



12.268 
1.510 
2.142 
2.677 
3.541 
5.002 
1.399 
1.490 



[539] 



136 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Series 3 
1% inch Harris Pump 
Length of Eduction Pipe 19.32 feet 

Average lift 3.44 feet 
Average Submergence 82.19 per cent 
Supply of Compressed Air in Well Casing Connected with Air Main 





2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in 
cubic feet per second. 


Absolute pressure of 
air at gage, in pounds 
per sauare inch. 


Input, in foot pounds 
per second. 


Discharge of water, in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


' Submergence, in 
i per cent. 


Lift, in feet. 


Output, in foot pouuds 
\ per second. 


| Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
li inch tail piece. 


Coefficient of slip and 
pipe friction. 








1 

i 


W 

w 


q w 


q 

g 


s 


h . 


1 

o 


e 


% 


V 

i 


c 

p 


327 
328 
329 
330 
331 


.05765 
.05768 
.06303 
.10627 
.06635 


21.471 
21.483 
21.612 
21.936 
21.712 


49.705 
49.772 
55.230 
96.470 
58.835 


2.1052 
2.1097 
2.1391 
2.0774 
2.1220 


.03368 
.03375 
.03422 
.03324 
.03395 


15.118 
15.149 
15.360 
14.921 
15.238 


81.73 
81.76 
82.48 
82.55 
82.55 


3.530 
3.524 
3.385 
3.372 
3.372 


7.431 
7.434 
7.241 
7.004 
7.155 


14.950 
14.937 
13.411 
7.261 
12.161 


1.712 
1.709 
1.842 
3.197 
1.954 

























[540] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



137 



Series 4 
114 inch Harris Pump 
Length of Eduction Pipe 19.32 feet 

Average Lift 3.29 feet 
Average Submergence 82.97 per cent 
Supply of Compressed Air in Well Casing Shut off from Air Main 



1 


2 


3 


* 1 5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in 
cubic feet per second. 


Absolute pressure of 
air at gage, in pounds 
per square inch. 


Input, in foot pounds 
per second. 


Discharge of water, in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 


Ontput, in foot pounds 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
li in. tail piece. 


Coefficient of slip and 
pipe friction. 






Pg 






1w 


q g 


s 


hi 


i 


e 


q w 


v i 


c 

p 


332 
333 
334 
335 
336 
337 
338 
339 
340 
341 
342 


.02726 
.02727 
.04258 
.05678 
.07903 
.09331 
.11108 
.12428 
.14421 
.16332 
.02706 


21.257 
21.251 
21.281 
21.452 
21.788 
21.971 
22.330 
22.684 
23.202 
23.703 
21.251 


1 

23.127 1.7898 


.02864 
.03123 
.03329 
.03392 
.03324 
.03276 
.03221 
.03158 
.03072 
.02987 
.03120 


12.855 
14.017 
14.943 
15.226 
14.920 
14.704 
14.458 
14.174 
13.788 
13.407 
14.003 


83.64 
83.16 
82.54 
82.54 
82.54 
82.54 
82.54 
83.02 
83.36 
83.36 
83.36 


3.162 
3.254 
3.375 
3.375 
3.375 
3.375 
3.375 
3.286 
3.215 
3.215 
3.215 


5.659 
6.353 
7.023 
7.156 
7.012 
6.912 
6.795 
6.486 
6.173 
6.004 
6.270 


24.468 
27.485 
19.372 
14.506 
9.837 
8.056 
6.409 
5.293 
4.143 
3.409 
27.336 


0.952 
0.873 
1.279 
1.674 
2.378 
2.848 
3.449 
3.936 
4.694 
5.465 
0.867 










36.257 
49.327 
71.280 
85.790 
106.020 
122.530 
149.000 
176.120 
22.937 


2.0810 
2.1202 
2.0777 
2.0479 
2.0135 
1.9738 
1.9200 
1.8673 
1.9503 











































[541] 



138 



BULLETIN OF THE UNIVERSITY OP WISCONSIN 



Series 5 

l 1 /! inch Annular Air Tube System 
Length of Eduction Pipe 19.32 feet 

Average Lift 3.02 feet 
Average Submergence 84.37 per cent 



>3 03 



3 -9 



w d 

0/ ,.H 

fa 03 03 

D o3 o3 

o * 50 



as 



18 



.22 ° 



S 3 



a? 



10 



12 



O O) 

fig 



.03372 
.05340 
.08921 
.11202 
.12910 
.15505 
.02775 
.04712 
.07736 
.07427 
.11310 
.13194 
.16106 
.12755 
.06910 
.03324 



22.130 
22.294 
22.418 
22.542 
22.559 
22.707 
21.988 
22.105 
22.300 
22.166 
22.307 
22.360 
22.401 
22.366 
22.195 
21.947 



31.545 
50.940 
86.120 
109.380 
126.280 
153.930 
25.663 
44.045 
73.850 
70.760 
109.220 
128.130 
156.890 
123.950 
66.000 
30.910 



0.2956 
0.4434 
0.7380 
0.8776 
0.9404 
1.0808 
0.2430 
0.3658 
0.6236 
0.5484 
0.8128 
0.8865 
1.0688 
0.8892 
0.5542 
.3322 



.00473 
.00709 
.01181 
.01404 
.01504 
.01729 
.00389 
.00585 
.00998 
.00877 
.01300 
.01418 
.01710 
.01423 



.00531 



2.123 
3.182 
5.300 
6.301 
6.750 
7.760 
1.746 
2.626 
4.479 
3.936 
5.835 
6.364 
7.675 
6.387 
3.981 



83.70 
85.54 
86.00 
84.47 
84.73 
84.10 
85.07 
86.16 
86.36 
85.28 
84.27 
82.48 
80.19 
82.96 
85.48 
S3. 98 



3.149 
2.794 
2.705 
3.001 
2.950 
3.072 
2. 
2.67E 
2. 
2.844 
3.040 
3.3S5 
3.828 
3. 
2.805 
3.095 



0.931 
1.239 
1.996 
2.634 
2.774 
3.321 
0.701 
0.978 
1.644 
1.560 
2.471 
3.001 
4.091 
2.927 
1.554 
1.028 



2.951 
2.432 
2.318 
2.408 
2.197 
2.158 
2.732 
2.222 
2.226 
2.204 
2.262 
2.343 
2.609 
2.362 
2.355 
3.326 



7.129 
7.532 
7.554 
7.978 
8.584; 
8.96S 
7.134 
8.055 
7.751 
8.469 
8.700 
9.304 
9. 418 
8.964 
7.791 
6.2(0 



542] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



139 



Series 6 
iy± inch Harris Pump 
Length of Eduction Pipe 19.32 feet 
Average Lift 11.40 feet 
Average Submergence 40.97 per cent 
Well Casing open to Atmosphere 



03 C 
r 

i s 3 



bog 



£ 0) 







o 3 



U> i-S 



is 



3 
O 
Q 

O 

o 

S! 



O a) 



o 9 



13 



is .2 



Co 

.2'£ 

a! Q 
Q 3 



359 
360 
361 
362 
363 
364 
365 
366 
367 
368 
369 



.16245 
.15727 
.14641 
.13339 
.11566 
.10565 
.09236 
.07979 
.06059 
.04214 
.02258 



20.205 
20.040 
19.735 
19.393 
19.045 
18.821 
18.609 
18.421 
18.108 
18.020 
17.943 



118.600 
112.020 
99.620 
85.770 
69.870 
61.410 
51.420 
42.718 
30.240 
20.630 
10.795 



.6603 
.6584 
.6904 
.6714 
.6801 
.6879 
.6819 
.6911 
.6700 
.6307 
.4668 



.01056 
.01053 
.01105 
.01074 
.01088 
.01101 
.01091 
.01106 
.01072 
.01009 
.00747 



4.739 
4.726 
4.959 
4.820 
4.883 
4.941 
4.896 
4.964 
4.811 
4.528 
3.353 



40.36 
40.36 
41.12 
40.43 
41.11 
40.90 
40.84 
41.04 
41.10 
41.38 
42.06 



11.522 
11.522 
11.376 
11.509 
11.378 
11.419 
11.430 
11.392 
11.380 
11.326 
11.194 



7.608 
7.586 
7.853 
7.727 
7.738 
7.854 
7.794 
7.873 
7.624 
7.144 
5.225 



6.415 
6.773 
7.883 
9.009 
11.075 
12.790 
15.156 
18.432 
25.212 
34.637 
48.402 



15.384 
14.934 
13.251 
12.419 
10.630 
9.596 
8.465 
7.215 
5.652 
4.177 
3.023 



[543] 



140 



BULLETIN OP THE UNIVERSITY OF WISCONSIN 



Series 7 
1% inch Harris Pump 
Length of Eduction Pipe 19.32 feet 
Average Lift 10.88 feet 
Average Submergence 43.66 per cent 
Supply of Compressed Air in Well Casing shut off from Air Main 



>3 03 



Ik 



CO g 



o 

af ® 

M fat 
<D cs ec 

S+j O 1 

o ro M 

oB v, ft 

^caa 



ps 
o 
a 
+3 

o . 

.3 8 

-03 

in 

a© 
a a 



03 £ 

« o 

£ 03 



^^2 
^3 =1 



-rH 8 

iT Q 



P- 03 
«H Q, 

o rf 



TO 

OP 
t« rj 

5° 



03 rj 



TO 8 



s ° 

.5 a 



10 



•rH q 

a^ 

Is 



li 



12 



03 .-, 

O 03 

eS O 



w 



13 



03 8 
£.2 



>s'c3 



370 
371 
372 
373 
374 
375 
376 
377 
378 
379 



.15286 
.14442 
.13800 
.12812 
.11721 
.10433 
.09344 
.08294 
.07054 
.05435 



20.153 
19.988 
19.818 
19.602 
19.333 
19.118 
18.924 
18.753 
18.559 
18.376 



110.730 

102.250 
95.200 
83.840 
73.180 
62.750 
54.160 
46.535 
37.980 
28.142 



.7500 

.7566 
.7533 
.7627 
.7646 
.7695 
.7702 
.7715 
.7707 
.7407 



.01200 
.01211 
.01205 
.01220 
.01223 
.01231 
.01232 
.01234 
.01233 
.01185 



5.386 
5.435 
5.408 
5.475 
5.489 
5.525 
5.529 
5.538 
5.534 
5.318 



43.36 
43.50 
43.50 
43.63 
43.63 
43.63 
43.76 
43.76 
43.69 
43.69 



10.943 
10.916 
10.916 
10.891 
10.891 
10.891 
10.866 
10.866 
10.879 
10.879 



8.208 
8.259 
8.223 
8.306 
8.327 
8.380 
8.369 
8.382 
8.384 
8.058 



7.411 

8.077 
8.638 
9.907 
11.379 
13.355 
15.452 
18.015 
22.076 
28.632 



12.738 
11.926 
11.453 
10.503 
9.584 
8.474 
7.585 
6.722 
5.722 
4.587 



[544] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



141 



Series 8 
1% inch Harris Pump 
Length of Eduction Pipe 26.74 feet 

Average Lift 15.70 feet 
Average Submergence 41.29 per cent 
Well Casing open to Atmosphere 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in 
cubic feet per second. 


Absolute pressure of 
air at gage, in pounds 
per square inch. 


Input, in foot pounds j 
per second. 


Discharge of water, in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a ; 
li in. tail piece. 


Coefficcient of slip and 
pipe friction. 




\ 


8 


1 

i 


w 

w 


q 

w 




s 


h 


1 

o 


e 


q a 
<*w 


V 

i 


c 

P 


381 


.02768 


18.661 


15.559 


.3528 


.00564 


2.531 


43.92 


14.997 


5.291 


34.007 


4.908 


0.(6 


1 

.3 54 


383 


.05711 


19.363 


36.595 


.7094 


.01135 


5.094 


40.76 
40.76 


15.842 


11.238 


30.710 


5.032 






384 


.08941 


19.770 


61.190 


.7340 


.01174 


5.269 


15.842 


11.628 


19.005 


7.617 


1.38 


.0943 


385 


.09389 


19.858 


65.140 


.7377 


.01180 


5.296 


40.76 


15.842 


11.687 


17.942 


7.957 


1.39 


.0917 


386 


.11082 


20.135 


80.280 


.7278 


.01164 


5.225 


40.76 


15.842 


11.530 


14.363 


9.520 


1.37 


.1058 


387 


.12442 


20.424 


94.540 


.7451 


.01192 


5.349 


41.16 


15.735 


11.724 


12.402 


10.438 


1.40 


.0779 


388 


.13729 


20.683 


107.980 


.7423 


.01188 


5.333 


41.16 


15.735 


11.680 


10.818 


11.557 






389 


.15024 


21.013 


123.230 


.7396 


.01183 


5.309 


41.16 


15.735 


11.638 


9.444 


12.700 


1.39 


.0700 


390 


.16155 


21.267 


136.950 


.7374 


.01180 


5.297 


41.16 


15.735 


11.603 


8.473 


13.689 


1.39 


.0667 



[545] 



142 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Series 9 
114 inch Harris Pump 
Length of Eduction Pipe 26.74 feet 

Average Lift 16.02 feet 
Average Submergence 40.08 per cent 
Supply of Compressed Air in Well Casing Connected with Air Main 



•S-o 
- a 



» fl s 

fa a> o 

s 

® bt 3 

ft 



T3 
S3 

o 
a 

+^ 

o . 

^ S3 

.3 8 

S3 a 



© S3 

|§ 

o 



^ s 



"SB 



ft ft 



S3 



10 



S3 S3 
O 

O M 



11 



12 



O 0) 

> a 

o o 



13 



£ 0) 

<w'3 

|i 

<D-t* 



O O' 

l-g 

a 



391 


.16016 


19.557 


107.040 


.7180 


.01149 


5.157 


37.73 


16.652 


11.955 


11.168 


13. £33 


392 


.15329 


19.557 


102.420 


0.7240 


.01158 


5.197 


37.98 


16.585 


12.007 


11.723 


13V239 


39S 


.13558 


19.557 


90.640 


0.7443 


.01191 


5.345 


38.70 


16.392 


12.201 


13.461 


11.384 


394 


.12313 


19.695 


84.150 


0.7995 


.01279 


5.740 


39.93 


16.062 


12.842 


15.261 


9.(27 


395 


.10836 


19.736 


74. 5C0 


0.8229 


.01316 


5.906 


40.57 


15.892 


13.078 


17.540 


8.234 


396 


.09476 


19.689 


64.770 


0.7779 


.01244 


5.584 


40.48 


15.917 


12.382 


19.119 


7.617 


397 


.08192 


19.695 


56.060 


0.7592 


.01215 


5.453 


41.31 


15.695 


11.914 


21.252 


6.743 


398 


.06941 


19.677 


47.337 


0.7549 


.01208 


5.421 


41.17 


15.732 


11.875 


25.086 


5.746 


399 


.03867 


19.194 


23.978 


0.5848 


.00936 


4.201 


41.37 


15.678 


9.168 


38.236 


4.131 


400 


.02735 


19.170 


17.127 


0.4817 


.00771 


3.4C0 


41.61 


15.614 


7.521 


43.917 


3.547 



1.C0 
1.55 



1.43 
1.42 



.0574 

.06:1 



.0951 
.10:0 



[546] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



14S 



Series 10 
1% inch Harris Pump 
Length of Eduction Pipe 26.74 feet 

Average Lift 15.73 feet 
Average Submergence 41.19 per cent 
Supply of Compressed Air in Well Casing Shut off from Air Main 



o S 



a be 

<D 03 

4J bi 
o* 3 



E3 

a 

O 

a 

o . 
c o 



a£ 



— 

O 3 

CO o 

£ a 



a^ 
•~ a 



■Ss 



£ a 

o3 a 

be M 

^a 

22 



a 

<D • 
JIB'S 
Sh « 

a p, 



10 



al 

o 



12 



si 

3o 



^3 



it 



13 



Oh 



14 



05 

•a a' 
o o 

a o 

a) 

c »• 

Oq 



401 


.01865 


19.022 


11.537 


0.3038 


.00486 


2.181 


40.97 


15.785 


4.796 


41.567 


402 


.04614 


19.034 


28.611 


0.6384 


.01021 


4.582 


39.63 


16.143 


10.306 


36.025 


403 


.07618 


19.553 


51.610 


0.7530 


.01205 


5.409 


41.01 


15.775 


11.878 


23.015 


404 


.08477 


19.717 


58.975 


0.7474 


.01196 


5.368 


41.12 


15.745 


11.768 


19.955 


405 


.10125 


19.925 


72.620 


0.7510 


.01201 


5.390 


41.06 


15.761 


11.836 


16.298 


406 


.11055 


20.142 


81.810 


O.7530 


.01205 


5.408 


41.27 


15.706 


11.827 


14.456 


407 


.12091 


20.360 


92.140 


0.7544 


.01207 


5.418 


41.45 


15.657 


11.810 


12.818 


409 


.14969 


21.150 


126.280 


0.8007 


.01281 


5.749 


42.99 


15.245 


12.207 


9.667 



3.838 
4.519 
6.322 
7.089 
8.431 
9.175 
10.018 
11.684 



1.40 
1.41 



1.42 



.1434' 



.0956 
.0875 



[547] 



144 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Series 11 
iy± inch Harris Pump 
Length of Eduction Pipe 26.74 feet 

Average Lift 4.74 feet 
Average Submergence 82.40 per cent 
Supply of Compressed Air in Well Casing Shut off from Air Main 



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410 


.02958 


23.922 


31.741 


2.1421 


.03427 


15.382 


82.35 


4.738 


10.148 


31.970 


411 


.05231 


24.058 


46.750 


2.3443 


.03751 


16.835 


81.99 


4.818 


11.294 


19.903 


412 


.06542 


24.141 


71.465 


2.3288 


.03726 


16.723 


81.99 


4.818 


11.219 


15.698 


413 


.08416 


24.388 


93.740 


2.3073 


.03692 


16.570 


81.99 


4.818 


11.116 


11.858 


414 


.10138 


24.641 


115.150 


2.2683 


.03629 


16.287 


82.38 


4.713 


10.691 


9.284 


415 


.11222 


24.771 


128.770 


2.2322 


.03571 


16.028 


82.42 


4.702 


10.495 


8.150 


416 


.11977 


24.901 


138.673 


2.2166 


.03546 


15.916 


82.42 


4.702 


10.422 


7.516 


417 


.13375 


25.137 


157.680 


2.1740 


.03478 


15.611 


82.72 


4.622 


10.047 


6.373 


418 


.14417 


25.278 


171.580 


2.1475 


.03436 


15.422 


82.58 


4.659 


10.004 


5.831 


419 


.15856 


25.550 


192.480 


2.0996 


.03359 


15.078 


82.58 


4.659 


9.782 


5.033 


420 


.16968 


25.832 


209. 94' 


2.0798 


.03327 


14.933 


83.01 


4.544 


9.450 


4.502 



0.863 
1.395 
1.756 
2.280 
2.794 
3.143 
3.378 
3.846 
4.196 
4.721 
5.101 







4.41 


.0334 


4.33 


.0331 


4.19 


.0317 






4.03 


.0294 


3.91 


.0279 



[548] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



145 



Series 12 
1% inch Harris Pump 
Length of Eduction Pipe 26.74 feetr 

Average Lift 4.48 feet 
Average Submergence 83.26 per cent 
Supply of Compressed Air in Well Casing Connected with Air Main 



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421 


.16317 


24.712 


186.370 


2.1658 


.03465 


15.553 


82.49 


4.683 


10.142 


5.442 


422 


.15415 


24.741 


176.400 


2.1868 


.03499 


15.705 


82.47 


4.688 


10.253 


5.812 


423 


.14477 


24.730 


165.560 


2.2125 


.03540 


15.889 


82.47 


4.688 


10.372 


6.265' 


424 


.13803 


24.844 


159.990 


2.2821 


.03651 


16.386 


83.86 


4.317 


9.851 


6.157 


425 


.13260 


24.821 


153.400 


2.2855 


.03657 


16.413 


83.90 


4.307 


9.843 


6.417 


426 


.11900 


24.791 


137.400 


2.3079 


.03692 


16.570 


83.85 


4.318 


9.965 


7.253 


427 


.11414 


24.796 


131.860 


2.3125 


.03700 


16.606 


84.00 


4.279 


9.895 


7.504 


428 


.09308 


24.C08 


106.060 


2.3414 


.03746 


16.813 


83.71 


4.357 


10.202 


9.619 


429 


.06418 


24.260 


71.120 


2.4001 


.03840 


17.235 


83.51 


4.410 


10.584 


14.882 


430 


.04296 


23.942 


46.425 


2.2523 


.03604 


16.178 


82.33 


4.726 


10.643 


22.927 



4.709 
4.406 
4.090 
3.781 
3.626 
3.223 
3.085 
2.485 
1.671 
1.192 



10 



[549] 



146 



BULLETIN OF THE UNIVERSITY OP WISCONSIN 



Series 13 
114 inch Harris Pump 
Length of Eduction Pipe 26.74 feet 

Average Lift 4.79 feet 
Average Submergence 82.23 per cent 
7.5 feet of 2-inch Pipe at Upper End of Eduction Pipe 



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431 

432 
433 
434 
435 
436 
437 
438 
439 
440 



.04783 
.06223 
.07868 
.08575 
.09630 
.10791 
.11888 
.12994 
.14444 
.15295 



23.751 
23.857 
24.011 
24.175 
24.305 
24.500 
24.706 
24.883 
25.137 
25.390 



51.890 
68.090 
87.120 
96.240 
109.170 
124.140 
138.920 
153.870 
174.020 
187.650 



2.6378 
2.6902 
2.6972 
2.7064 
2.6881 
2.6668 
2.6265 
2.6145 
2.5808 
2.5544 



.04220 
.04307 
.04315 
.04330 
.04301 
.04267 
.04202 
.04183 
.04129 
.04087 



18.941 
19.331 
19.367 
19.434 
19.303 
19.153 
18.859 
18.775 
18.532 
18.343 



81.70 
81.60 
81.60 
82.14 
82.14 
82.44 
82.68 
82.68 
82.68 
82.68 



4.922 
4.922 
4.773 
,4.773 
4.698 
4.632 
4.632 
4.632 
4.632 



12.911 
13.241 
13.274 
12.918 
12.830 
12.528 
12.165 
12.109 
11.952 
11.832 



24.883 
19.449 
15.237 
13.425 
11.753 
10.092 



1.134 
1.445 
1.824 
1.981 

2.239 
2.529 



8.756! 2.829 
7.869 3.106 
3.498 
3.743 



[550] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



147 



Series 14 
114 inch Harris Pump 

Length of Eduction Pipe 41.50 feet 
Average Lift 7.66 feet 

Average Submergence 81.54 per cent 



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.04628 
.05673 
.07710 
.09321 
.11178 
.12360 
.13504 
.15065 
.16503 
.17810 



29.119 
29.160 
29.030 
29.431 
29.656 
29.786 
29.974 
30.268 
30.374 
30.598 



68.780 
84.550 
114.120 
140.730 
170.630 
189.750 
209.100 
236.490 
260.350 
283.800 



2.6318 
2.7047 
2.7174 
2.7895 
2.7721 
2.7549 
2.7230 
2.6775 
2.6510 
2.6162 



.04211 
.04327 
.04348 
.04463 
.04435 
.04408 
.04356 
.04284 
.04241 
.04186 



18.900 
19.421 
19.515 
20.032 
19.905 
19.784 
19.551 
19.228 
19.033 
18.788 



81.57 
81.53 
80.24 
81.71 
81.68 
81.68 



7.650 
7.670 
8.200 
7.590 
7.602 
7.602 



81.68 7.602 

81.68 7.602 

81.68 7.602 

81.96 7.487 



20.132 
20.743 
22.281 
21.171 
21.073 
20.940 
20.700 
20.353 
20.153 
19.588 



29.270 
24.532 
19.525 
15.043 
12.350 
11.035 
9.899 
8.607 
7.741 
6.902 



1.099 
1.311 
1.773 
2.089 
2.520 
2.804 
3.100 
3.517 
3.892 
4.255 



5.12 


.0184 


5.02 


.0166 


4.98 


.0173 


4.91 


.0217 



[551] 



148 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Series 15 
lYi inch Harris Pump 

Length of Eduction Pipe 41.50 feet 
Average Lift 23.47 feet 

Average Submergence 43.45 per cent 



1 


2 


3 


4 


5 


5 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in 
cubic feet per second. 


Absolute pressure of 
air at gage, in pounds 
per square inch. 


Input, in foot pounds 
per second. 


Discharge of water in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
1 gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 


Output, in foot pounds 1 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
U in. tail piece. 


Coefficient of slip and 
pipe friction. 






Pg 


ii 


w 

w 


<lw 


q g 


s 


h i 


i 


e 


% 


v i 


c 

P 


452 


.04608 


22.184 


41.703 


0.7579 


.01213 


5.445 


41.99 


24.075 


18.245 


43.755 


3.799 


1.43 


.1001 


453 


.06119 


22.260 


55.850 


0.8763 


.01402 


6.292 


41.88 


24.121 


21.138 


37.850 


4.365 


1.65 


.0745 


454 


.09139 


22.906 


89.060 


1.0502 


.01680 


7.540 


42.67 


23.793 


24.984 


28.052 


5.441 


1.97 


.0506 


455 


.11442 


23.259 


114.990 


1.0613 


.01698 


7.621 


43.68 


23.372 


24.808 


21.573 


6.739 


1.99 


.0462 


456 


.13427 


23.536 


138.320 


1.0515 


.01682 


7.549 




23.345 


24.548 


17.745 


7.983 


1.98 


.0431 


457 


.14235 


23.814 


150.900 


1.0752 


.01720 


7.719 


43.97 


23.252 


25.C01 


16.567 


8.276 


2.02 


.0414 


458 


.14586 


23.897 


155.720 


1.0732 


.01717 


7.706 


44.13 


23.187 


24.882 


15.979 


8.495 


2.02 


.0410 


459 


.15958 


24.120 


173.410 


1.0652 


.01704 


7.647 


44.19 


23.161 


24.670 


14.227 


9.365 


2.00 


.0391 


460 


.17384 


24.350 


192.570 


1.0468 


.01675 


7.518 


44.82 


22.900 


23.970 


12.447 


10.389 


1.98 


.0378 



[552] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



149 



Series 16 
iy± inch Indiana Pump 
Length of Eduction Pipe 42.08 feet 

Average Lift 24.20 feet 
Average Submergence 42.50 per cent 



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.06385 


22.504 


61.980 


0.9346 


.01495 


6.710 


42.78 


24.079 


22.504 


36.308 


4.272 


462 


.08435 


22.734 


83.580 


1.0533 


.01685 


7.563 


42.40 


24.239 


25.525 


30.540 


5.008 


463 


.10107 


22.893 


101.700 


1.0839 


.01734 


7.782 


42.25 


24.304 


26.342 


25.903 


5.829 


464 


.11530 


23.135 


118.660 


1.0359 


.01737 


7.795 


42.41 


24.236 


26.318 


22.178 


6.638 


465 


.13223 


23.447 


139.650 


1.0842 


.01735 


7.787 


42.19 


24.327 


26.375 


18.837 


7.022 


466 


.03937 


22.562 


38.830 


0.6931 


.01109 


4.977 


43.56 


23.753 


16.462 


42.400 


3.550 


467 


.05899 


22.556 


58.300 


0.9791 


.01566 


7.028 


42.79 


24.077 


23.573 


40.435 


3.767 


468 


.08997 


22.775 


90.630 


1.1111 


.0177* 


7.980 


42.22 


24.313 


27.013 


29.807 


5.0(0 


469 


.12171 


23.346 


128.870 


1.1309 


.01 80S 


8.119 


42.16 


24.340 


27.527 


21.360 


6.728 


470 


.16194 


24.236 


184.150 


0.9761 


.01562 


7.010 


42.25 


24.313 


23.730 


12.S86 


10.368 



[553] 



150 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Series 17 
1% inch Indiana Pump 
Length of Eduction Pipe 42.08 feet 

Average Lift 7.63 feet 
Average Submergence 81.95 per cent 



1 


2 


3 


4 


5 


Discharge of water, in | os 
cubic feet per second. | 


7 


8 


9 


10 


11 


i Ratio of volume of air I ^ 
1 to volume of water. j M 


Velocity of water in a i- 
li in. tail piece. 03 


Coefficient of slip and | M 
pipe friction. j 


1 Number of run. 


Quantity of free air in 
cubic feet per second. 


Absolute pressure of 
air at gage, in pounds 
per square inch. 


Imput, in foot pounds 
per second. 


[ 

Discharge of water, in 
pounds per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 1 
per cent. 


! Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. ' 






Vg 


ii 


w 

w 


q w 


q g 


s 


h l 


\> 


e 


% 
<l'w 


v i 


c 

P 


471 
472 
473 
474 
475 
476 
477 
478 
479 
480 


.02344 
.05683 
.08171 
.04650 
.09030 
.11778 
.14039 
.15713 
.16622 
.17769 


29.439 
29.514 
29.657 
29.568 
29.875 
30.179 
30.497 
30.545 
30.639 
30.957 


35.582 
86.570 
94.610 
71.010 
139.820 
185.180 
223.820 
251.080 
266.750 
289.040 


1.4842 
2.7549 
2.9091 
2.6282 
3.0043 
3.0259 
3.0078 
2.9306 
2.8738 
2.8758 


.02375 
.04407 
.04655 
.04205 
.04807 
.04841 
.04812 
.04689 
.04598 
.04601 


10.659 
19.780 
20.893 
18.873 
21.574 
21.727 
21.597 
21.046 
20.638 
20.650 


81.48 
81.48 
81.48 
81.88 
81.81 
81.82 
83.07 
81.98 
81.53 
83.00 


7.797 
7.797 
7.797 
7.627 
7.653 
7.652 
7.127 
7.587 
7.771 
7.533 


11.573 
21.480 
22.682 
20.045 
22.993 
23.153 
21.435 
22.235 
22.330 
21.661 


32.525 
24.814 
23.975 
28.230 
16.445 
12.503 
9.577 
8.855 
8.371 
7.494 


0.987 
1.290 
1.326 
1.106 
1.879 
2.433 
2.918 
3.352 
3.615 
3.862 















































[554] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



151 



Series 18 
1% inch Tee Pump 
Length of Eduction Pipe 41.60 feet 

Average Lift 6.58 feet 
Average Submergence 84.18 per cent 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in 
cubic feet per second. 


Absolute pressure of 
air at gage, in pounds 
per square inch. 


Imput, in foot pounds 
per second. 


Discharg-e of water, in 
pounds per second. 


Discharg-e of water, in 
cubic feet per second. 


Discharg-e of water, in 
gallons per minute. 


Submergence, in 
per cent. 


l 

Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
; to volume of water. 


Velocity of water in a 
li in. tail piece. 


Coefficient of slip and 
pipe friction. 




^a 


V g 


h 


w w 




% 


s 


h i 


\> 


e 


^a 


v i 


c 

P 


q w 


481 

482 
483 
484 
485 
486 
487 
488 
489 
490 


.02299 
.05188 
.08346 
.09323 
.11101 
.12285 
.12708 
.13555 
.14628 
.15770 


29.628 
29.598 
29.573 
29.739 
29.792 
29.898 
29.969 
30.033 
30.092 
29.757 


34.903 
78.650 
126.380 
142.220 
169.760 
188.850 
196.050 
209.630 
226.750 
239.990 


1.9931 
2.6369 
3.0145 
3.1033 
3.1251 
3.1300 
3.1373 
3.1325 
3.1325 
3.0489 


.03189 
.04219 
.04823 
.04965 
.05000 
.05008 
.05020 
.05011 
.05011 
.04878 


14.313 
18.937 
21.648 
22.283 
22.441 
22.478 
22.532 
22.491 
22.491 
21.893 


84.28 
84.11 
83.71 
84.28 
84.01 
84.30 
84.28 
84.18 
84.26 
84.40 


6.540 
6.605 
6.777 
6.540 
6.645 
6.529 
6.542 
6.580 
6.556 
6.487 


13.034 
17.417 
20.427 
20.295 
20.765 
20.435 
20.524 
20.610 
20.535 
19.777 


37.345 
22.146 
16.163 
14.270 
12.232 
10.821 
10.469 
9.832 
9.056 
8.240 


0.721 
1.230 
1.730 
1.878 
2.220 
2.453 
2.532 
2.705 
2.920 
3.194 















































[555] 



152 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



Series 19 
1% inch Tee Pump 
Length of Eduction Pipe 41.60 feet 

Average Lift 23.96 feet 
Average Submergence 42.40 per cent 



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IS 



£ft 

8ft 



491 


.03234 


21.930 


30.072 


0.6857 


.01097 


4.924 


42.74 


23.823 


16.333 


54.307 


2.948 




492 


.05557 


21.912 


51.610 


0.8762 


.01402 


6.292 


42.48 


23.929 


20.965 


40.620 


3.964 




493 


.08162 


22.083 


77.170 


1.0500 


.01680 


7.540 


42.62 


23.870 


25.063 


32.480 


4.859 




494 


.10163 


22.255 


97.700 


1.0883 


.01741 


7.813 


42.07 


24.103 


26.230 


26.847 


5.838 




495 


.12077 


22.384 


117.600 


1.0839 


.01734 


7.782 


42.36 


23.978 


25.990 


22.101 


6.965 




496 


.13632 


22.567 


135.350 


1.0817 


.01731 


7.769 


42.39 


23.965 


25.920 


19.150 


7.876 




497 


.14213 


22.673 


142.200 


1.0808 


.01729 


7.759 


42.33 


23.993 


25.930 


18.235 


8.221 




498 


.15487 


22.797 


156.960 


1.0742 


.01719 


7.715 


42.33 


23.992 


25.771 


16.419 


9.009 




499 


.16434 


22.879 


167.800 


1.0635 


.01701 


7.635 


42.26 


24.021 


25.548 


15.225 


9.662 




500 


.17430 


23.032 


180.380 


1.0552 


.01688 


7.576 


42.46 


23.939 


25.260 


14.004 


10.326 





[556] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



153 



Series 20 
inch Tee Pump 
Variable Length of Eduction Pipe 
Constant Lift of Five feet 
Variable Submergence 



CO y 



a-3 
s 5? 



CD CO CO 

-£ bp 3 

3 ^ a 

o 

£.3 CD 



c? a 



3 

o 
a 
+? 

o . 



3 -H 

Q CD 



® a 
I 8 

P CD 



cot3 
a 3 



.3? 

to 73 
fi in 
^ 0) 



CO ^ 

5° 



«3 
co 3 

Jl 
co 3 

-fi.2 



8 



10 



.s « 

o 



12 



O co 

f~ 

fi O 

o © 

«H 3 

11 



q 



501 


.17902 


16.433 


60.830 


0.3049 


.00488 


2.190 


30.00 


5.00 


1.524 


2.510 


37.968 


502 


.16960 


16.350 


55.760 


0.3125 


.00500 


2.244 


30.00 




1.562 


2.802 


33.920 


503 


.16610 


16.244 


52.325 


0.3012 


.00485 


2.177 


30.00 




1.506 


2.878 


34.251 


504 


.15602 


16.091 


45.873 


0.3044 


.00482 


2.163 


30.00 




1.522 


3.318 


32.372 


505 


.14962 


16.047 


43.429 


0.3077 


.00492 


2.208 


30.00 




1.538 


3.543 


30.412 


506 


.12849 


15.820 


33.365 


0.2950 


.00472 


2.118 


30.00 




1.475 


4.421 


27.224 


507 


.11937 


15.649 


28.262 


0.2755 


.00441 


1.979 


30.00 




1.387 


4.910 


27.068 


508 


.11257 


15.407 


23.040 


0.2294 


.00367 


1.647 


30.00 




1.147 


4.978 


30.670 


509 


.07932 


15.284 


14.843 


0.1887 


.00302 


1.355 


30.00 




0.943 


6.357 


26.267 


510 


.17903 


16.826 


60.830 


0.3192 


.00511 


2.293 


30.00 




1.596 


2.624 


35.040 


511 


.12482 


16.690 


40.513 


0.3178 


.00508 


2.280 


30.00 




1.589 


3.920 


24.574 


512 


.14870 


16.412 


42.588 


0.2960 


.00474 


2.127 


30.00 


»» 


1.480 


3.475 


31.372 


513 


.10607 


15.948 


24.097 


0.2650 


.00424 


1.903 


30.00 




1.325 


5.500 


25.017 


514 


.08495 


15.694 


16.548 


0.2142 


.00343 


1.539 


30.00 




1.071 


6.470 


24.768 


515 


.06883 


15.586 


12.361 


0.1686 


.00270 


0.990 


30.00 




0.843 


6.280 


47.800 


516 


.08477 


30.620 


134.890 


3.5600 


.05700 


25.583 


88.00 




17.800 


13.220 


1.487 


517 


.16847 


31.551 


278.850 


3.5100 


.05620 


25.224 


88.00 




17.550 


6.295 


2.998 


518 


.16530 


31.544 


273.600 


3.5350 


.05660 


25.403 


88.00 




17.675 


6.465 


2.921 


519 


.15052 


31.364 


247.140 


3.5880 


.05740 


25.760 


88.00 




17.440 


7.065 


2.622 


520 


.12154 


30.898 


195.670 


3.6000 


.05760 


25.850 


88.00 




18.000 


9.210 


2.110 



[557] 



154 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

Series 20 — Continued 
114 inch Tee Pump 
Variable Length of Eduction Pipe 
Constant Lift of Five feet 
Variable Submergence 



1 


2 


3 


4 


5 


6 




8 


9 


10 


11 


12 


13 


14 


Number of run. 


Quantity of free air, in | 
I cubic feet per second, j 


Absolute pressure of 
air at gage, in pounds 
per square inch. 


Input, in foot pounds 
per second. 


Discharge of water, in 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
li in. tail piece. 


Coefficient of slip and 
pipe friction. 






Pg 




w 

w 


q w 


% 


s 


h i 




e 


i» 


v i 


c 

p 



521 


.09058 


30.628 


144.220 


3.5350 


.05660 


25.403 


88.00 


5.00 


17.675 


12.222 


1.601 


522 


.07174 


30.463 


113.400 


3.4220 


.05480 


24.596 


88.00 


>1 


17.110 


15.100 


1.309 


523 


.05023 


30.365 


79.020 


3.1620 


.05070 


22.756 


88.00 




15.810 


20.150 


0.991 


524 


.04619 


30.365 


72.660 


3.0940 


.04950 


22.170 


88.00 


II 


15.470 


21.280 


0.933 


525 


.03906 


30.316 


61.373 


2.9400 


.04700 


21.095 


88.00 




14.700 


23.980 


0.831 


526 


.05982 


30.463 


94.560 


3.3100 


.05300 


23.788 


88.00 


)l 


16.550 


17.500 


1.129 


527 


.07484 


30.537 


118.590 


3.4600 


.05540 


24.867 


88.00 




17.300 


14.600 


1.351 


528 


.09855 


30.761 


157.850 


3.2380 


.05180 


23.250 


88.00 




16.190 


10.270 


1.903 


529- 


.13623 


31.151 


221.870 


3.2640 


.05230 


23.473 


88.00 




16.320 


8.070 


2. 605 


530 


.13872 


23.941 


149.380 


2.5910 


.04152 


18.637 


80.00 




12.955 


8.672 


3.341 


531 


.13235 


23.888 


142.510 


2.6112 


.04185 


18.784 


80.00 




13.056 


9.161 


3.163 


532 


.13120 


23.862 


140.300 


2.6180 


.04196 


18.832 


80.00 


II 


13.090 


9.330 


3.127 


533 


.12688 


23.771 


134.450 


2.6387 


.04229 


18.980 


80.00 




13.194 


9.815 


3.001 


534 


.11800 


23.713 


124.500 


2.6387 


.04229 


18.980 


80.00 




13.194 


10.600 


2.790 


535 


.10855 


23.587 


113.160 


2.6457 


.04240 


19.030 


80.00 




13.228 


11.690 


2.560 


536 


.09870 


23.507 


102.330 


2.6528 


.04251 


19.082 


80.00 




13.264 


12.962 


2.322 


537 


.09180 


23.458 


94.650 


2.6528 


.04251 


19.082 


80.00 




13.264 


14.014 


2.159 


538 


.08328 


23.385 


85.380 


2.6457 


.04240 


19.030 


80.00 




13.228 


15.492 


1.964 


539 


.07144 


23.295 


72.700 


2.6180 


.04196 


18.831 


80.00 




13.090 


18.008 


1.703 


540 


.06130 


23.225 


62.020 


2.1 5511 


[ .04089 


18.352 
[55c 


: so.oo 

i] 




12.755 


20.575 


1.499 



DAYIS & WEIDNER — THE AIR LIFT PUMP 



155 



Series 20 — Continued 
114 inch Tee Pump 
Variable Length of Eduction Pipe 
Constant Lift of Five feet 
Variable Submergence 



3 

3 O 

a 



O 3 

3 a 2 



<D 6ud 3 

CO 

,0 d ft. 



II 



w 

-3 3 

O o 

.2 a 



.3 3 

; o 

0) 0) 

2 * 

°^ 

&=£ 
IS « 

-3.Q 
3 

«> n 



^ 3 

^3 

£3 

O CD 

« a 

fH 3 

c3 O 

! be 



8 



as 



10 



.a s 

o 

p CO 

3 M 

ft ^ 

3 a 
o 



11 



12 



"cS ^ 

O el 
CO £ 

a^ 

3 O 

r-t CD 



^5 

o > 

'is 
« 



13 



£ft 

•H _ 

>»+3 



<X>rH 



.04929 
.03443 
.04877 
.16334 
.15805 
.14968 
.14369 
.13967 
.13330 
.10339 
.11514 
.10590 
.09700 
.08380 
.07253 
.05421 



.02937 
.15917 
.15302 



23.157 49.520 
23.092 34.3SO 



23.128 
24.281 



48.920 
181. lio! 
20. 577 | 124. 330; 

20.446 116.010 

I 

20.363 110.010 
20.283105.810 



9.820 
6.200 



20.202 
20.092 

20.013 

I 

19.889, 75.780 



19.797 
19.661 
19.595 
19.500 



68.520 
57.910 
49.630 
36.510 



19.. 583 46.930 
20.416; 22.650 
19.480 108.300 
19. 3S3 102.250 



1.9610 
2.2222 
2.4040 
2.5643 
1.8293 
1.8422 
1.8 
1.8383 
1.8: 
1.8658 
1.8728 
1.8658 
1.8728 
1.8728 
1.8451 
1.7986 
1.8451 
1.4750 
1.5580 
1.5480 



.03143 
.03562 



.04110 

.02932 
.02952 
.02946 
.02946 
.02946 
.02990 
.03001 
.02990 
.03001 
.03001 
.02957 
.02882 
.02957 
.02364 
.02497 
.02481 



14.104 

15.984 

17.2 

18.447 

13.155 

13.250 

13.221 

13.221 

13.221 

13.418 

13.470 

13.418 

13.470 

13.470 

13.257 

12.935 

13.244 

10.610 

11.208 

11.136 



80.00 
80.00 
80.00 
80.00 
70.00 
70.00 
70.00 
70.00 
70.00 
70.00 
70.00 
70.00 
70.00 
70.00 
70.00 
70.00 
70.00 
70.00 
65.00 
65.00 



5.00 



9.805 
11.111 

12.020 
12.822 
9.146 
9.211 
9.191 
9.191 
9.191 
9.329 
9.364 
9.329 
9.364 
9.364 
9.225 
8.993 
9.225 
7.375 
7.790 
7.740 



19.805 
32.323 
24.575 
7. 
7.357 
7.941 
8.356 
8.688 
9.210 
12.243 
11.150 
12.310 
13.670 
16*. 170 
18.590 
24.630 
19.670 
32.560 
7.192 
7.570 



1.568 
0.967 
1.267 
3. 
5. 
5.070 
4.877 
4.741 
4.525 
3.458 
3.837 
3.542 
3.232 
2.792 
2.453 
1.881 
2.322 
1.242 
6.376 
6.168 



[559] 



156 



BULLETIN OP THE UNIVERSITY OF WISCONSIN 

Seeies 20 — Continued 
ly^ inch Tee Pump 
Variable Length of Eduction Pipe 
Constant Lift of Five feet 
Variable Submergence 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


Number of run. 


Quantity of free air in ( 
cubic feet per second. | 


Absolute pressure of 
air at gage, in pounds 
per square inch. 


Input, in foot pounds i 
per second. 


Discharge of water in 1 
pounds per second. 


Discharge of water, in 
cubic feet per second. 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


; Lift in feet. 


I Output, in foot pounds 
per second. 


Efficiency, in per cent. 


I Ratio of volume of air 
to volume of water. ! 




^a 


Pg 


] i 


w w 




% 


s 


h l 




e 


% 
















561 


.14462 


19.244 


94.430 


1.5530 


.02489 


11.172 


65.00 


5.00 


7.765 


8.234 


5.810 


562 


.13850 


19.178 


89.460 


1.5770 


.02528 


11.347 


65.00 




7.885 


8.814 


5.480 


563 


.12730 


19.028 


80.220 


1.5770 


.02528 


11.347 


65.00 




7.885 


9.828 


5.036 


564 


.11986 


18.906 


73.680 


1.5720 


.02519 


11.306 


65.00 




7.860 


10.670 


4.760 


565 


.10973 


18.791 


66.200 


, 1.5770 


.02528 


11.347 


65.00 




7.885 


11.912 


4.342 


566 


.10100 


18.676 


59.620 


1.5820 


.02535 


11.378 


65.00 




7.910 


13.268 


3.984 


567 


.09206 


18.585 


53.440 


1.5970 


.02559 


11.486 


65.00 




7.985 


14.942 


3.593 


568 


.07798 


18.433 


43.780 


1.5770 


.02528 


11.347 


65.00 




7.885 


18.010 


3.019 


569 


.06224 


18.299 


33.980 


1.5430 


.02473 


11.100 


65.00 




7.715 


22.702 


2.517 


570 


.04100 


18.212 


22.080 


1.4620 


.02343 


10.516 


65.00 




7.310 


33.107 


1.7:0 


571 


.02666 


18.131 


14.047 


1.2340 


.01978 


8.869 


65.00 




6.170 


43.950 


0.634 


572 


.14218 


18.708 


81.440 


1.2820 


.02053 


9.214 


60.00 




6.410 


7.871 


6.926 


573 


.14089 


18.649 


79.890 


1.2920 


.02070 


9.290 


60.00 




6.4C0 


8.087 


6.807 


574 


.14441 


18.605 


80.900 


1.2920 


.02070 


9.290 


eo.oo 




6.4C0 


7.985 


6.977 


575 


.13696 


18.555 


76.090 


1.2765 


.02045 


9.178 


60.00 




6.382 


8.388 


6.697 


576 


.12870 


18.454 


70.030 


1.2887 


.02065 


9.267 


60.00 




6.443 


9.201 


6.233 


577 


.12064 


18.343 


64.270 


1.3020 


.02086 


9.362 


60.00 




6.510 


10.130 


5.784 


578 


.10852 


18.201 


55.940 


1.3160 


.02110 


9.470 


60.00 




6.580 


11.763 


5.144 


579 


.09120 


18.013 


44.940 


1.2903 


.02068 


9.281 


CO. 00 




6.451 


14.336 


4.410 


580 


.07681 


17.865 


36.530 


1.2820 


.02055 


9.223 


eo.oo 




6.410 


17.55C 


3.738 



[560] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



157 



Series 20 — Continued 
iy± inch Tee Pump 
Variable Length of Eduction Pipe 
Constant Lift of Five feet 
Variable Submergence 



1 


o 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


Number of run. 


' Quantity of free air, in 
cubic feet per second. 


Absolute pressure of 
air at gage, in pounds 
per souare inch. 


Input, in footpounds 
per second. 


Discharge of water, in 
pounds per second. 


Discharge of water, in 1 
cubic feet per second. 1 


Discharge of water, in 
gallons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 


Output, in foot pounds 
per second. 


Efficiency, in per cent. 


i Ratio of volume of air 
1 to volume of water. 




^a 


p g 


>i 


w w 




^g 


s 


n l 


] o 


e 


o 

q w 


581 


.06479 


17.742 


29.810 


1.2500 


.0200: 


8.990 


60.00 


5.00 


6.250 


20.968 


3.235 


582 


.04248 


17.624 


18.980 


1.1363 


.0182] 


8.173 


60.00 




5.681 


29.935 


2.333 


583 


.03024 


17.005 


11.250 


0.9757 


.01563 
.01422 


7.015 

6.382 


60.00 
50.00 




4.878 


43.365 




584 


.15900 


17.896 


74.070 


0.8870 




4.435 


5.994 


11.180 


585 


.16970 


17.997 


81.000 


0.8811 


.01412 


6.337 


50.00 




4.405 


5.336 


12.020 


586 


.15541 


17.789 


70.630 0.887O 


.01422 


6.382 


50.00 




4.435 


6.280 


10.930 


587 


.14218 


17.679 


62.440 


0.8870 


.01422 


6.382 


50.00 




4.435 


7.103 


9.9C0 


588 


.13527 


17.563 


57.330 


0.8811 


.01412 


6.337 


50.00 




4.405 


7.684 


9.5S6 


589 


.12915 


17.434 


52.970 


0.8788 


.01408 


6.319 


50.00 




4.394 


7.840 


9.174 


590 


.11692 


17.308 


45.990 


0.8646 


.01386 


6.220 


50.00 




4.323 


9.390 


8.439 


591 


.10560 


17.196 


40.300 


0.8824 


.01414 


6.346 


50.00 




4.412 


10.940 


7.482 


592 


.08915 


17.003 


32.000 


0.8427 


.01351 


6.064 


50.00 




4.213 


13.170 


6.236 


593 


.07646 


16.905 


26.010 


0.8310 


.01332 


5.978 


50.00 




4.155 


15.900 


5.740 


594 


.05662 


16.806 


18.810 


0.7834 


.01256 


5.637 


50.00 




3.917 


20.820 


4.580 


595 


.02661 


16.632 


8.270 


0.5376 


.00862 


3.867 


50.00 




2.688 


32.500 


3.089 


596 


.15290 


17.075 


59.550 


0.5731 


.00918 


4.120 


40.00 




2.865 


4.814 


16.655 


597 


.14323 


16.922 


53.330 


0.5556 


.00890 


3.995 


40.00 




2.778 


5.209 


16.094 


598 


.14001 


16.898 


51.590 


0.5556 


.00890 


3.995 


40.00 




2.778 


5.385 


15.731 


599 


.13358 


16.773 


48.710 


0.5510 


.00883 


3.963 


40.00 




2.755 


5.656 


15.128 


600 


.13065 


1 16.733 


, 45.400 


j 0.5495 


.00881 


3.954 


40.00 




2.747 


6.053 


14.830 



.2 

CP 



[561] 



158 BULLETIN OF THE UNIVERSITY ' OF WISCONSIN 

Series 20 — Continued 
VA inch Tee Pump 
Variable Length of Eduction Pipe 
Constant Lift of Five feet 
Variable Submergence 



1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


1 

Number of run. 


Quantity of free air in 
cubic feet per second. 


Absolute pressure of i 
air at g-ag-e, in pounds 
per square inch. ; 


Input, in foot pounds 
per second. 


Discharg-e of water, in 
pounds per second. 


Discharg-e of water, in 
cubic feet per second. 


Discharg-e of water, in 
g-allons per minute. 


Submergence, in 
per cent. 


Lift, in feet. 

1 


Output, in footpounds 
per second. 


Efficiency, in per cent. 


Ratio of volume of air 
to volume of water. 


Velocity of water in a 
li in. tail piece. 


Coefficient of slip and 
pipe friction. 




% 




li 


W w 






s 


hi 


lo 


e 


Qa 


v i 


c 

p 




601 

602 
603 
604 
605 
606 
607 
608 


.12152 
.11320 
.09990 
.08929 
.07830 
.06226 
.05360 
.03978 


16.588 
16.450 
16.356 
16.205 
16.107 
15.994 
15.864 
15.796 


39.910 
35.660 
29.760 
24.890 
20.930 
15.690 
32.590 
8.960 


0.5450 
0.5391 
0.5319 
0.4914 
0.4762 
0.4386 
0.3704 
0.3058 


.00873 
.00864 
.00852 
.00788 
.00763 
.00703 
.00594 
.00490 


3.918 
3.878 
3.824 
3.536 
3.424 
3.155 
2.666 
2.199 


40.00 
40.00 
40.00 
40.00 
40.00 
40.00 
40.00 
40.00 




2.725 
2.695 
2.659 
2.457 
2.381 
2.193 
1.852 
1.529 


6.828 
7.K9 
8.936 
9.871 
11.375 
13.980 
14.710 
17.065 


13.920 
13.102 
11.727 
11.330 
10.263 
8.856 
9.320 
8.119 







































[562] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



159 



TABLE II 

LOSS DUE TO FRICTION IN AIR PIPE AND NOZZLE WHEN DISCHARGING INTO 

THE ATMOSPHERE 

Series I 



Run. 


Quantity of 
free air in cubic 
feet per second. 


Loss of head 
in pounds per 
square inch. 


279 


.13253 


.658 


280 


.14018 


.750 


281 


.12336 


.585 


282 


.11439 


.490 


283 


.09530 


.855 


284 


.10438 


.416 


285 


.07792 


.225 


286 


.08059 


.238 


287 
288 


.08597 
.07052 


.282 
.208 


289 


.06264 


.160 


290 


.07025 


.186 


291 


.05847 


.126 


292 


.04926 


.091 


293 


.05392 


.117 


294 


.04071 


.061 


295 


.03697 


.004 


296 


.01951 


.001 



[563] 



160 



BULLETIN OF THE UNIVERSITY OF WISCONSIN 



TABLE III 

LOSS DUE TO FRICTION IN AIR PIPE AND NOZZLE WHEN DISCHARGING INTO 
THE ATMOSPHERE 

Series 2-13 inclusive 



Run. 


Quantity of 
free air in cubic 
i'eet per second. 


Loss of head 
in pounds per 
square inch. 


1 


.05860 


0.4185 


2 


.07510 


0.6424 


3 


.09098 


0.9490 


4 


.11035 


1.3556 


5 


.12047 


1.6090 


6 


.12978 


1.8095 


7 


.13847 


2.0924 


8 


.14710 


2.2986 


9 


.15367 


2.4695 


10 


.16303 


2.8527 



TABLE IV 

LOSS DUE TO FRICTION IN AIR PIPE AND NOZZLE WHEN DISCHARGING INTO 
THE ATMOSPHERE 

Series 14 and 15 



Run. 


Quantity of 
free air in cubic 
feet per second. 


Loss of head 
in pounds per 
square inch. 


1 


.02347 


0.0825 


2 


.04092 


0.2358 


3 


.07531 


0.6071 


4 


.09119 


0.8605 


5 


.10425 


1.1022 


6 


.11822 


1.4086 


7 


.13095 


1.6621 


S 


.14068 


1.9215 


9 


.15153 


2.1750 


10 


.16493 


2.5521 



[564] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



161 



BIBLIOGRAPHY 

Gerlach. Zeitschrift des Vereines Deutscher Ingenieure, Vol. 
29, p. 311, April, 1885. A letter to the editor saying that 
the first air lift experiments were performed by Loscher in 
1797. 

Siemens, Werner. "A New Method of Lifting Water. " Pro- 
ceedings Institute of Civil Engineers, Vol. 81, p. 400,, 
1881-85, part 3. Article abstracted from Dingier 's Poly- 
technische Journal, Vol. 256, p. 284, 1885. Describes a 
method for draining a mining shaft by sinking wells around 
the shaft and pumping by means of the air lift. 

Browne, R. E. and Behr H. C. "Dr. Pohle's Air Lift Pump." 
Transactions of the Technical Society of the Pacific Coast, 
Vol. 8, Feb. 1890. See p. 112 of this bulletin. 

"The Air Lift Pump." Engineering News, Vol. 29, p. 541, 
June, 1893. Good article on the history and development, 
advantages, record of patents, brief and elementary discus- 
sion of the theory, data and results of Browne and Behr 
experiments. 

Merriam, L. B. "A Test of the Pohle Air Lift Pump at De- 
Kalb, 111." Engineering News, Vol. 32, p. 26, July, 1894. 
Data and discussion of a test on a 6-inch central air pump. 
Best condition of submergence obtained at 48 per cent., an 
efficiency of 17.48 per cent, based on the power delivered 
to the compressor was obtained. Lift 133 feet. 

"Raising Water by the Air Lift." Engineering Record, Vol. 
31, p. 363, April, 1895, and Vol. 32, p. 26, June, 1895. His- 
tory and development, advantages, several examples of 
plants in operation, detailed description of the Rockford, 
111., plant. 

Loweth, C. F. "The Air Lift at Waseca, Minn." Engineering 
Record, Vol. 32, p. 120, June, 1895. Short description with 
plan of plant. 



11 



[565] 



162 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

Harris, E. G. "The Theory of the Air Lift Pump." Journal 
of the Franklin Institute, Vol. 140, p. 32, July, 1895. One 
of the first of the theoretical discussions that have been 
published. See p. 20 of this bulletin. 

Murray, George R. "Some Figures on the Cost of Pumping 
with the Pohle Air Lift." Compressed Air, Vol. 1, p. 166, 

1896. An estimate on the cost and operation of an air lift 
plant. 

Kinealy, J. H. "Experiments to Determine the Efficiency of 
the Air Lift Pump." Engineering News, Vol. 37, p. 185, 
March, 1897. A letter to the editor giving the discharge 
curve of a small model pump, lift 6 inches. 

"Tests of the Pohle Air Lift Pumps at Rockford, 111., Water 
"Works." Engineering News, Vol. 37, p. 140, March, 1897. 
A reliable test of a plant consisting of four wells, which 

I showed an efficiency of 24 per cent, based on the I. H. P. 
in the compressor. Data given. 

Johnson, E. E. "Deep Well Pumping." Journal of the West- 
ern Society of Engineers, Vol. 2, p. 169, March, 1897. A 
valuable paper comparing the air lift with other types of 
deep well pumps. 

Johnson, E. E. "Theoretical and Practical Limitations of the 
Air Lift Pump." Engineering News, Vol. 37, p. 250, April, 

1897. An interesting article in which the author assumes 
that the pump operates by a volume of air displacing an 
equal volume of water. Tables and diagrams showing 
theoretical horse power required to lift one cubic foot of 
water from various depths, when air is compressed either 
isothermally, adiabatically or two stage compression, and 
the power required by the air lift. A duty table is also 
given. 

Harris, E. G. "The Efficiency of the Air Lift Pump." Engi- 
neering News, Vol. 37, p. 282, May, 1897. A letter to the 
editor commenting on Mr. Johnson's article. A list of con- 
ditions which modify the action of the pump is given. 

Ledoux, J. W. "A Deep Well Pumping Plant at Waukesha, 
Wis." Engineering Record, Vol. 37, p. 543, May, 1898. A 
comparison between the efficiency of the air lift pump and 
steam deep well pump. Data for test given. Discussion 

[566] 



DAVIS & WEIDNER— -THE AIR LIFT PUMP 



163 



of this article by Mr. H. T. Abrams on page 569, Vol. 37, 
and page 54, Vol. 38. An answer by Mr. Ledoux to the 
discussion, Vol. 38, p. 10. June, 1898. 
Davis, F. A. W. " Test of Lifting Water from Wells with Air. ' ' 
Journal of the New England Water Works Association, 
Vol. 13, p. 51, June, 1898. Also in Proceedings American 
Water Works Association, p. 21, June, 1898. Data for a 
test on 10-inch central air tube well, in which the percent- 
age of submergence, rate of pumping, and type of air inlet 
was varied. 

Mead, D. W. "Deep Well Pumping Machinery. " Proceedings 
American Water Works Association, p. 146, 1898. Some 
figures on the duty of air lift pumps. 

Josse, E. "Druckluft-Wasserheber. " Zeitschrift des Vereines 
Deutscher Ingenieure, Vol. 42, p. 981, Sept., 1898. A valu- 
able article giving results of experiments on an experi- 
mental pump and also on actual wells. See p. 112 of this 
bulletin. 

"The Air Lift." Engineering Record, Vol. 38, p. 317, Sept., 
1898. Discusses the method of piping the wells, energy 
losses in compression. Gives data of the test made by Mr. 
F. A. W. Davis. 

"The Air Lift." Engineering record, Vol. 38, p. 401, October, 
1898. A translation of Prof. Josse 's article in Zeitschrift 
des Vereines Deutscher Ingenieure. 

"The Mammoth Pump." Proceedings Institute of Civil Engi- 
neers, Vol. 140, p. 323, 1899-1900, part 2. Abstract of 
Prof. Josse 's article. 

"An Air Lift Pump." American Engineer and Railroad Jour- 
nal, p. 27, Jan., 1900. Details and description of plant 
supplying railroad shops and road tanks. 

Wiles, C. W. "Supplying Water from Deep Wells by Com- 
pressed Air." Proceedings American Water Works As- 
sociation, p. 22, 1900. A general description of the air lift 
with examples of operating plants. 

Rix, Edward A. "Pumping by Compressed Air." Journal of 
the Association of Engineering Societies. Vol. 25, p. 173, 
October, 1900. A paper discussing different methods of 
pumping by compressed air, among which is the air lift 

[567] 



164 BULLETIN OF THE UisIVERSITY OP WISCONSIN 

pump. Data for some tests and a table of general require- 
ments for air lift pumping. 

' Moving Water Horizontally by Air Lift Pumps at Point 
Pleasant, Va." Engineering News, Vol. 54, p. 359, Nov., 
1900. An interesting description of a plant in which the 
water is pumped up an embankment rising 67 feet in a hori- 
zontal distance of 410 feet. 

"Air Lift Pump on the London Central Railway. " Compressed 
Air, Vol. 7, p. 1936, August, 1902. Brief description of the 
plant. 

"Water Supply from Deep Wells by Air Power." Compressed 
Air, Vol. 7, p. 1970, Sept., 1902. Advantages of a diverg- 
ing eduction pipe explained. 

"Pressluft-Pumpen Fur Wasserf orderung. " Der Hydrotekt, 
Vol. 1, p. 202, Dec, 1902. A general description of the 
pump and its advantages, with a discussion of Josse's ex- 
periments and his method of computing efficiency. 

Maxwell, Wm. H. "The Raising of Water from Deep Wells 
and Borings by Compressed Air." Transactions of the 
British Association of Waterworks Engineers, Vol. 8, p. 
70, July, 1903. Data and discussion of tests at Tunbridge 
Wells, England. Most economical percentage of submerg- 
ence found to be between 69 and 75 per cent. An efficiency 
of 64 per cent., based on I. H. P. of air cylinder, and 36.8 
per cent, based on I. H. P. of steam cylinder was obtained. 
Lift about 120 feet. 

Friedrich, G. C. H. "Lifting Water by Compressed Air." The 
Engineer (Cleveland), Vol. 40, p. 547, July, 1903. Gives 
results of practical experience with hints for construction. 

"Air Lift Pumps." The Engineer (London), Vol. 96, p. 568, 
Dec, 1903. Also in Compressed Air, Vol. 9, p. 2890, April, 
1904. An abstract of an article by L. Darapsky in the 
Berg und Huttenmannischen Zeitung, No. 11, 1903. In 
the original a large portion of the article is devoted to the 
consideration of the claims of rival patentees and decisions 
in the German law courts. A good historical and descrip- 
tive article. 

Bjorling, P. R. "Raising Water with Compressed Air." Mu- 
nicipal Journal and Engineer, Vol. 15, p. 245, Dec, 1903. 

[568] 



DAVIS & WEIDNER — THE AIR LIFT PUMP 



165 



Describes several methods of pumping by compressed air, 
among which is a descriptive article on the air lift. 

Friedrick, G. C. H. "River Wells and the Horizontal Delivery 
of Water." The Engineer (Chicago), Vol. 41, p. 435, June, 
1904. Description of a plant taking its water supply from 
a river and discharging through a horizontal distance of 
511 feet in a vertical lift of 60 feet. 

Wittrock. "Verwendung von Druckluft zum Heben von 
Fliissigkeiten. " Zeitschrift des Vereines Deutscher In- 
genieure, Vol. 48, p. 1080, July, 1904. Descriptive article 
of several European plants. 

"The Air Lift." The Engineer (Chicago), Vol. 41, p. 564, 
Aug., 1904. An illustrated article describing the operation, 
methods of piping wells, multiple lifts, etc. Empirical 
formulas advanced for volume of air required, capacity, 
ratio of area of air pipe to water pipe. 
.Goff, A. H. "Data Relating to the Air Lift." The Engineer, 
(Chicago), Vol. 41, p. 811, Dec, 1904. Two tables giving 
ratio of water to air required, volume of free air, air press- 
ure,, submergence, and horse power for different lifts. 

"Air Lift Pumping Plant of the Redlands Water Co." Engi- 
neering Record, Vol. 51, p. 8, January, 1905. A descrip- 
tion of the plant and data for a 48 hour test. 

"A 300 Foot Cold Storage Air Lift." Municipal Journal and 
Engineer, Vol. 18, p. 150, March, 1905. Short descriptive 
article. 

"Notes on Air Lifts for Raising Water." Engineering Record, 
Vol. 52, p. 44, Dec, 1905. A practical article compiled 
from the Ingersoll-Rand Co. catalogue. The following 
subjects are discussed, theory of the air lift pump, Frizell 
system, Pohle system, economy, cost of pumping, limita- 
tions of the system, methods of piping the wells, and ar- 
rangement of wells and piping. 

Friedrich, G. C. H. "Air Lift Pumping." The Engineer 
(Chicago), Vol. 43, p. 373, June, 1906. Description of a 
well that was tested and some data for use in the construc- 
tion of an air lift. 

Kelly, James. "On the Raising of Water by Compressed Air 
at Preesall, Lancashire." Proceedings of the Institute of 

[569] 



166 BULLETIN OF THE UNIVERSITY OF WISCONSIN 

Civil Engineers, Yol. 163, p. 353, 1905-06, part 1. Abstract 
in American Machinist, Vol. 29, p. 203, Aug., 1906, part 2. 
Also in Engineering Record, Yol. 54, p. 243, Sept., 1906. 
A valuable paper, see p. 113 of this bulletin. 

Darapsky, L. and Schubert, F. "Die Wirkungsweise der 
Pressluftpumpen. " Zeitschrift des Vereines Deutscher 
Ingenieure, Vol. 50, p. 2062, Dec, 1906. A valuable article 
giving data, analysis and discussion of laboratory and 
commercial tests. Empirical formulas derived. See p. 
114 of this bulletin. 

"Air Lift for Brine.' ' Power, Vol. 27, p. 71, Jan., 1907. An 
answer to an inquiry for the design of an air lift for pump- 
ing brine. 

Gibson, A. H. "Hydraulics and its Applications.' ' A briei 
article in a text-book on Hydraulics, p. 674, giving a de- 
scription and the theory of the pump. D. Van Nostrand 
Co., New York, 1908. 

"Test of an Air Lift Pump and Experimental Studies of Air 
Lift Pumps." Engineering News, Yol. 59, p. 666, June, 

1908. A report of a duty test made on the Atlantic City 
plant, and the description and results of the "Westinghouse 
Air Brake Go's, experiments. See p. 115 of this bulletin. 

Lorenz, H. "Die Arbeitsweise und Berechnung der Druckluft- 
Fhlssigkeitsheber. " Zeitschrift des Vereines Deutscher 
Ingenieure, Vol. 53, p. 545, April. 1909. A valuable mathe- 
matical analysis. See p. 24 of this bulletin. 

Ivens, E. M. "Tests Upon Compressed Air Pumping Systems 
of Oil Wells." Journal of the American Society of Me- 
chanical Engineers, Vol. 31, p. 341, March, 1909. A de- 
scription of some air lift plants in the Louisiana oil fields 
and various methods of piping the wells. Data for some 
tests. 

Green, L. M. "Efficiency of the Air Lift as a Solution Pump." 
Engineering and Mining Journal, Vol. 88, p. 251, Aug., 

1909. Discusses mathematically the theory of the air lift, 
amount of air required, minimum air pressure, efficiency 
of lift under given conditions. See p. 29 of this bulletin. 

' ' Algae as a Result of Air Lift Pumping. ' ' Engineering Record, 
Vol. 61, p. 277, March, 1910. Article states that the method 

[570] 



DAVIS & WEIDNER— THE AIR LIFT PUMP 



167 



of pumping the wells at Frankfort, Ind., was changed on 
account of the excessive growth of algae, which was 
thought to be due to the air lift. 
Harris, E. G. ' ' Compressed Air." McGraw-Hill Book Co., 
New York, 1910. An excellent chapter on the air lift pump, 
in which the following topics are elaborated: (1) Theory, 
(2) Design, (3) Use as a dredge pump, (4) Testing wells 
with the air lift, (5) Data on operating air lifts. 



[571] 



I t> 0.. 'D 



\ 



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Pressboard 




Pamphlet 
Binder 
Gaylord Bros. 
Makers 
Syracuse, N. Y. 
PAT. JAN 21. 1908 



An investigation of the air li sci 
533.5D262 C.2 




3 12bB D3CH5 5321